Multi-material decomposition using statistical image reconstruction for spectral CT

Isotopic gamma lines for identification of shielding materials

Identifying the constituting materials of concealed objects is crucial in a wide range of sectors, such as medical imaging, geophysics, nonproliferation, national security investigations, and so on. Existing methods face limitations, particularly when multiple materials are involved or when there are challenges posed by scattered radiation and large areal mass. Here we introduce a novel brute-force statistical approach for material identification using high spectral resolution detectors, such as HPGe. The method relies upon updated semianalytic formulae for computing uncollided flux from source of gamma radiation, shielded by a sequence of nested spherical or cylindrical materials. These semianalytical formulae make possible rapid flux estimation for material characterization via combinatorial search through all possible combinations of materials, using a high-resolution HPGe counting detector. An important prerequisite for the method is that the geometry of the objects is known (for example, from X-ray radiography). We demonstrate the viability of this material characterization technique in several use cases with both simulated and experimental data in spherical geometry.

Feasibility study of YSO/SiPM based detectors for virtual monochromatic image synthesis

BACKGROUND

The development of photon-counting CT systems has focused on semiconductor detectors like cadmium zinc telluride (CZT) and cadmium telluride (CdTe). However, these detectors face high costs and charge-sharing issues, distorting the energy spectrum. Indirect detection using Yttrium Orthosilicate (YSO) scintillators with silicon photomultiplier (SiPM) offers a cost-effective alternative with high detection efficiency, low dark count rate, and high sensor gain.

OBJECTIVE

This work aims to demonstrate the feasibility of the YSO/SiPM detector (DexScanner L103) based on the Multi-Voltage Threshold (MVT) sampling method as a photon-counting CT detector by evaluating the synthesis error of virtual monochromatic images.

METHODS

In this study, we developed a proof-of-concept benchtop photon-counting CT system, and employed a direct method for empirical virtual monochromatic image synthesis (EVMIS) by polynomial fitting under the principle of least square deviation without X-ray spectral information. The accuracy of the empirical energy calibration techniques was evaluated by comparing the reconstructed and actual attenuation coefficients of calibration and test materials using mean relative error (MRE) and mean square error (MSE).

RESULTS

In dual-material imaging experiments, the overall average synthesis error for three monoenergetic images of distinct materials is 2.53% ±2.43%. Similarly, in K-edge imaging experiments encompassing four materials, the overall average synthesis error for three monoenergetic images is 4.04% ±2.63%. In rat biological soft-tissue imaging experiments, we further predicted the densities of various rat tissues as follows: bone density is 1.41±0.07 g/cm3, adipose tissue density is 0.91±0.06 g/cm3, heart tissue density is 1.09±0.04 g/cm3, and lung tissue density is 0.32±0.07 g/cm3. Those results showed that the reconstructed virtual monochromatic images had good conformance for each material.

CONCLUSION

This study indicates the SiPM-based photon-counting detector could be used for monochromatic image synthesis and is a promising method for developing spectral computed tomography systems.

CT in musculoskeletal imaging: still helpful and for what?

Computed tomography (CT) is a common modality employed for musculoskeletal imaging. Conventional CT techniques are useful for the assessment of trauma in detection, characterization and surgical planning of complex fractures. CT arthrography can depict internal derangement lesions and impact medical decision making of orthopedic providers. In oncology, CT can have a role in the characterization of bone tumors and may elucidate soft tissue mineralization patterns. Several advances in CT technology have led to a variety of acquisition techniques with distinct clinical applications. These include four-dimensional CT, which allows examination of joints during motion; cone-beam CT, which allows examination during physiological weight-bearing conditions; dual-energy CT, which allows material decomposition useful in musculoskeletal deposition disorders (e.g., gout) and bone marrow edema detection; and photon-counting CT, which provides increased spatial resolution, decreased radiation, and material decomposition compared to standard multi-detector CT systems due to its ability to directly translate X-ray photon energies into electrical signals. Advanced acquisition techniques provide higher spatial resolution scans capable of enhanced bony microarchitecture and bone mineral density assessment. Together, these CT acquisition techniques will continue to play a substantial role in the practices of orthopedics, rheumatology, metabolic bone, oncology, and interventional radiology.

Self-supervised tomographic image noise suppression via residual image prior network

Computed tomography (CT) denoising is a challenging task in medical imaging that has garnered considerable attention. Supervised networks require a lot of noisy-clean image pairs, which are always unavailable in clinical settings. Existing self-supervised algorithms for suppressing noise with paired noisy images have limitations, such as ignoring the residual between similar image pairs during training and insufficiently learning the spectrum information of images. In this study, we propose a Residual Image Prior Network (RIP-Net) to sufficiently model the residual between the paired similar noisy images. Our approach offers new insights into the field by addressing the limitations of existing methods. We first establish a mathematical theorem clarifying the non-equivalence between similar-image-based self-supervised learning and supervised learning. It helps us better understand the strengths and limitations of self-supervised learning. Secondly, we introduce a novel regularization term to model a low-frequency residual image prior. This can improve the accuracy and robustness of our model. Finally, we design a well-structured denoising network capable of exploring spectrum information while simultaneously sensing context messages. The network has dual paths for modeling high and low-frequency compositions in the raw noisy image. Additionally, context perception modules capture local and global interactions to produce high-quality images. The comprehensive experiments on preclinical photon-counting CT, clinical brain CT, and low-dose CT datasets, demonstrate that our RIP-Net is superior to other unsupervised denoising methods.

Image-domain material decomposition for dual-energy CT using unsupervised learning with data-fidelity loss

BACKGROUND

Dual-energy computed tomography (DECT) and material decomposition play vital roles in quantitative medical imaging. However, the decomposition process may suffer from significant noise amplification, leading to severely degraded image signal-to-noise ratios (SNRs). While existing iterative algorithms perform noise suppression using different image priors, these heuristic image priors cannot accurately represent the features of the target image manifold. Although deep learning-based decomposition methods have been reported, these methods are in the supervised-learning framework requiring paired data for training, which is not readily available in clinical settings.

PURPOSE

This work aims to develop an unsupervised-learning framework with data-measurement consistency for image-domain material decomposition in DECT.

METHODS

The proposed framework combines iterative decomposition and deep learning-based image prior in a generative adversarial network (GAN) architecture. In the generator module, a data-fidelity loss is introduced to enforce the measurement consistency in material decomposition. In the discriminator module, the discriminator is trained to differentiate the low-noise material-specific images from the high-noise images. In this scheme, paired images of DECT and ground-truth material-specific images are not required for the model training. Once trained, the generator can perform image-domain material decomposition with noise suppression in a single step.

RESULTS

In the simulation studies of head and lung digital phantoms, the proposed method reduced the standard deviation (SD) in decomposed images by 97% and 91% from the values in direct inversion results. It also generated decomposed images with structural similarity index measures (SSIMs) greater than 0.95 against the ground truth. In the clinical head and lung patient studies, the proposed method suppressed the SD by 95% and 93% compared to the decomposed images of matrix inversion.

CONCLUSIONS

Since the invention of DECT, noise amplification during material decomposition has been one of the biggest challenges, impeding its quantitative use in clinical practice. The proposed method performs accurate material decomposition with efficient noise suppression. Furthermore, the proposed method is within an unsupervised-learning framework, which does not require paired data for model training and resolves the issue of lack of ground-truth data in clinical scenarios.

CT Material Decomposition using Spectral Diffusion Posterior Sampling

In this work, we introduce a new deep learning approach based on diffusion posterior sampling (DPS) to perform material decomposition from spectral CT measurements. This approach combines sophisticated prior knowledge from unsupervised training with a rigorous physical model of the measurements. A faster and more stable variant is proposed that uses a "jumpstarted" process to reduce the number of time steps required in the reverse process and a gradient approximation to reduce the computational cost. Performance is investigated for two spectral CT systems: dual-kVp and dual-layer detector CT. On both systems, DPS achieves high Structure Similarity Index Metric Measure(SSIM) with only 10% of iterations as used in the model-based material decomposition(MBMD). Jumpstarted DPS (JSDPS) further reduces computational time by over 85% and achieves the highest accuracy, the lowest uncertainty, and the lowest computational costs compared to classic DPS and MBMD. The results demonstrate the potential of JSDPS for providing relatively fast and accurate material decomposition based on spectral CT data.

One-step inverse generation network for sparse-view dual-energy CT reconstruction and material imaging

Objective.Sparse-view dual-energy spectral computed tomography (DECT) imaging is a challenging inverse problem. Due to the incompleteness of the collected data, the presence of streak artifacts can result in the degradation of reconstructed spectral images. The subsequent material decomposition task in DECT can further lead to the amplification of artifacts and noise.Approach.To address this problem, we propose a novel one-step inverse generation network (OIGN) for sparse-view dual-energy CT imaging, which can achieve simultaneous imaging of spectral images and materials. The entire OIGN consists of five sub-networks that form four modules, including the pre-reconstruction module, the pre-decomposition module, and the following residual filtering module and residual decomposition module. The residual feedback mechanism is introduced to synchronize the optimization of spectral CT images and materials.Main results.Numerical simulation experiments show that the OIGN has better performance on both reconstruction and material decomposition than other state-of-the-art spectral CT imaging algorithms. OIGN also demonstrates high imaging efficiency by completing two high-quality imaging tasks in just 50 seconds. Additionally, anti-noise testing is conducted to evaluate the robustness of OIGN.Significance.These findings have great potential in high-quality multi-task spectral CT imaging in clinical diagnosis.

Accurate Reconstruction of Multiple Basis Images Directly From Dual Energy CT Data

OBJECTIVE

We develop optimization-based algorithms to accurately reconstruct multiple ( 2) basis images directly from dual-energy (DE) data in CT.

METHODS

In medical and industrial CT imaging, some basis materials such as bone, metals, and contrast agents of interest are confined often spatially within regions in the image. Exploiting this observation, we develop an optimization-based algorithm to reconstruct, directly from DE data, basis-region images from which multiple ( 2) basis images and virtual monochromatic images (VMIs) can be obtained over the entire image array.

RESULTS

We conduct experimental studies using simulated and real DE data in CT, and evaluate basis images and VMIs obtained in terms of visual inspection and quantitative metrics. The study results reveal that the algorithm developed can accurately and robustly reconstruct multiple ( 2) basis images directly from DE data.

CONCLUSIONS

The developed algorithm can yield accurate multiple ( 2) basis images, VMIs, and physical quantities of interest from DE data in CT.

SIGNIFICANCE

The work may provide insights into the development of practical procedures for reconstructing multiple basis images, VMIs, and physical quantities from DE data in applications. The work can be extended to reconstruct multiple basis images in multi-spectral or photon-counting CT.

An Image-Based Prior Knowledge-Free Approach for a Multi-Material Decomposition in Photon-Counting Computed Tomography

Photon-counting CT systems generally allow for acquiring multiple spectral datasets and thus for decomposing CT images into multiple materials. We introduce a prior knowledge-free deterministic material decomposition approach for quantifying three material concentrations on a commercial photon-counting CT system based on a single CT scan. We acquired two phantom measurement series: one to calibrate and one to test the algorithm. For evaluation, we used an anthropomorphic abdominal phantom with inserts of either aqueous iodine solution, aqueous tungsten solution, or water. Material CT numbers were predicted based on a polynomial in the following parameters: Water-equivalent object diameter, object center-to-isocenter distance, voxel-to-isocenter distance, voxel-to-object center distance, and X-ray tube current. The material decomposition was performed as a generalized least-squares estimation. The algorithm provided material maps of iodine, tungsten, and water with average estimation errors of 4% in the contrast agent maps and 1% in the water map with respect to the material concentrations in the inserts. The contrast-to-noise ratio in the iodine and tungsten map was 36% and 16% compared to the noise-minimal threshold image. We were able to decompose four spectral images into iodine, tungsten, and water.

Evaluation of hafnium oxide nanoparticles imaging characteristics as a contrast agent in X-ray computed tomography

This research aimed to compare the quantitative imaging attributes of synthesized hafnium oxide nanoparticles (NPs) derived from UiO-66-NH2(Hf) and two gadolinium- and iodine-based clinical contrast agents (CAs) using cylindrical phantom. Aqueous solutions of the studied CAs, containing 2.5, 5, and 10 mg/mL of HfO2NPs, gadolinium, and iodine, were prepared. Constructed within a cylindrical phantom, 15 cc small tubes were filled with CAs. Maintaining constant mAs, the phantom underwent scanning at tube voltage variations from 80 to 140 kVp. The CT numbers were quantified in Hounsfield units (HU), and the contrast-to-noise ratios (CNR) were calculated within delineated regions of interest (ROI) for all CAs. The HfO2NPs at 140 kVp and concentration of 2.5 mg/ml exhibited 2.3- and 1.3-times higher CT numbers than iodine and gadolinium, respectively. Notably, gadolinium consistently displayed higher CT numbers than iodine across all exposure techniques and concentrations. At the highest tube potential, the maximum amount of the CAs CT numbers was attained, and at 140 kVp and concentration of 2.5 mg/ml of HfO2NPs the CNR surpassed iodine by 114%, and gadolinium by 30%, respectively. HfO2NPs, as a contrast agent, demonstrated superior image quality in terms of contrast and noise in comparison to iodine- and gadolinium-based contrast media, particularly at higher energies of X-ray in computed tomography. Thus, its utilization is highly recommended in CT.

Image Domain Multi-Material Decomposition Noise Suppression Through Basis Transformation and Selective Filtering

Spectral CT can provide material characterization ability to offer more precise material information for diagnosis purposes. However, the material decomposition process generally leads to amplification of noise which significantly limits the utility of the material basis images. To mitigate such problem, an image domain noise suppression method was proposed in this work. The method performs basis transformation of the material basis images based on a singular value decomposition. The noise variances of the original spectral CT images were incorporated in the matrix to be decomposed to ensure that the transformed basis images are statistically uncorrelated. Due to the difference in noise amplitudes in the transformed basis images, a selective filtering method was proposed with the low-noise transformed basis image as guidance. The method was evaluated using both numerical simulation and real clinical dual-energy CT data. Results demonstrated that compared with existing methods, the proposed method performs better in preserving the spatial resolution and the soft tissue contrast while suppressing the image noise. The proposed method is also computationally efficient and can realize real-time noise suppression for clinical spectral CT images.

Low-cost dual-energy CBCT by spectral filtration of a dual focal spot X-ray source

Dual-energy cone beam computed tomography (DE-CBCT) has been shown to provide more information and improve performance compared to a conventional single energy spectrum CBCT. Here we report a low-cost DE-CBCT by spectral filtration of a carbon nanotube x-ray source array. The x-ray photons from two focal spots were filtered respectively by a low and a high energy filter. Projection images were collected by alternatively activating the two beams while the source array and detector rotated around the object, and were processed by a one-step materials decomposition and reconstruction method. The performance of the DE-CBCT scanner was evaluated by imaging a water-equivalent plastic phantom with inserts containing known densities of calcium or iodine and an anthropomorphic head phantom with dental implants. A mean energy separation of 15.5 keV was achieved at acceptable dose rates and imaging time. Accurate materials quantification was obtained by materials decomposition. Metal artifacts were reduced in the virtual monoenergetic images synthesized at high energies. The results demonstrated the feasibility of high quality DE-CBCT imaging by spectral filtration without using either an energy sensitive detector or rapid high voltage switching.

Derivative-Free Iterative One-Step Reconstruction for Multispectral CT

Image reconstruction in multispectral computed tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. Existing methods necessitate computing the derivative of the forward map and potentially its regularized inverse. In this work, we present a simple yet highly effective algorithm for MSCT image reconstruction, utilizing iterative update mechanisms that leverage the full forward model in the forward step and a derivative-free adjoint problem. Our approach demonstrates both fast convergence and superior performance compared to existing algorithms, making it an interesting candidate for future work. We also discuss further generalizations of our method and its combination with additional regularization and other data discrepancy terms.

Systematic Review on Learning-based Spectral CT

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.

Quantitative multi-energy micro-CT: A simulation and phantom study for simultaneous imaging of four different contrast materials using an energy integrating detector

Emerging from the development of single-energy Computed Tomography (CT) and Dual-Energy Computed Tomography, Multi-Energy Computed Tomography (MECT) is a promising tool allowing advanced material and tissue decomposition and thereby enabling the use of multiple contrast materials in preclinical research. The scope of this work was to evaluate whether a usual preclinical micro-CT system is applicable for the decomposition of different materials using MECT together with a matrix-inversion method and how different changes of the measurement-environment affect the results. A matrix-inversion based algorithm to differentiate up to five materials (iodine, iron, barium, gadolinium, residual material) by applying four different acceleration voltages/energy levels was established. We carried out simulations using different ratios and concentrations (given in fractions of volume units, VU) of the four different materials (plus residual material) at different noise-levels for 30 keV, 40 keV, 50 keV, 60 keV, 80 keV and 100 keV (monochromatic). Our simulation results were then confirmed by using region of interest-based measurements in a phantom-study at corresponding acceleration voltages. Therefore, different mixtures of contrast materials were scanned using a micro-CT. Voxel wise evaluation of the phantom imaging data was conducted to confirm its usability for future imaging applications and to estimate the influence of varying noise-levels, scattering, artifacts and concentrations. The analysis of our simulations showed the smallest deviation of 0.01 (0.003-0.15) VU between given and calculated concentrations of the different contrast materials when using an energy-combination of 30 keV, 40 keV, 50 keV and 100 keV for MECT. Subsequent MECT phantom measurements, however, revealed a combination of acceleration voltages of 30 kV, 40 kV, 60 kV and 100 kV as most effective for performing material decomposition with a deviation of 0.28 (0-1.07) mg/ml. The feasibility of our voxelwise analyses using the proposed algorithm was then confirmed by the generation of phantom parameter-maps that matched the known contrast material concentrations. The results were mostly influenced by the noise-level and the concentrations used in the phantoms. MECT using a standard micro-CT combined with a matrix inversion method is feasible at four different imaging energies and allows the differentiation of mixtures of up to four contrast materials plus an additional residual material.

Prototyping optimization-based image reconstructions from limited-angular-range data in dual-energy CT

Image reconstruction from data collected over full-angular range (FAR) in dual-energy CT (DECT) is well-studied. There exists interest in DECT with advanced scan configurations in which data are collected only over limited-angular ranges (LARs) for meeting unique workflow needs in certain practical imaging applications, and thus in the algorithm development for image reconstruction from such LAR data. The objective of the work is to investigate and prototype image reconstructions in DECT with LAR scans. We investigate and prototype optimization programs with various designs of constraints on the directional-total-variations (DTVs) of virtual monochromatic images and/or basis images, and derive the DTV algorithms to numerically solve the optimization programs for achieving accurate image reconstruction from data collected in a slew of different LAR scans. Using simulated and real data acquired with low- and high-kV spectra over LARs, we conduct quantitative studies to demonstrate and evaluate the optimization programs and their DTV algorithms developed. As the results of the numerical studies reveal, while the DTV algorithms yield images of visual quality and quantitative accuracy comparable to that of the existing algorithms from FAR data, the former reconstruct images with improved visualization, reduced artifacts, and also enhanced quantitative accuracy when applied to LAR data in DECT. Optimization-based, one-step algorithms, including the DTV algorithms demonstrated, can be developed for quantitative image reconstruction from spectral data collected over LARs of extents that are considerably smaller than the FAR in DECT. The theoretical and numerical results obtained can be exploited for prototyping designs of optimization-based reconstructions and LAR scans in DECT, and they may also yield insights into the development of reconstruction procedures in practical DECT applications. The approach and algorithms developed can naturally be applied to investigating image reconstruction from LAR data in multi-spectral and photon-counting CT.

Performance evaluation of quantitative material decomposition in slow kVp switching dual-energy CT

BACKGROUND

Slow kVp switching technique is an important approach to realize dual-energy CT (DECT) imaging, but its performance has not been thoroughly investigated yet.

OBJECTIVE

This study aims at comparing and evaluating the DECT imaging performance of different slow kVp switching protocols, and thus helps determining the optimal system settings.

METHODS

To investigate the impact of energy separation, two different beam filtration schemes are compared: the stationary beam filtration and dynamic beam filtration. Moreover, uniform tube voltage modulation and weighted tube voltage modulation are compared along with various modulation frequencies. A model-based direct decomposition algorithm is employed to generate the water and iodine material bases. Both numerical and physical experiments are conducted to verify the slow kVp switching DECT imaging performance.

RESULTS

Numerical and experimental results demonstrate that the material decomposition is less sensitive to beam filtration, voltage modulation type and modulation frequency. As a result, robust material-specific quantitative decomposition can be achieved in slow kVp switching DECT imaging.

CONCLUSIONS

Quantitative DECT imaging can be implemented with slow kVp switching under a variety of system settings.

Image quality improvement of a one-step spectral CT reconstruction on a prototype photon-counting scanner

Objective. X-ray spectral computed tomography (CT) allows for material decomposition (MD). This study compared a one-step material decomposition MD algorithm with a two-step reconstruction MD algorithm using acquisitions of a prototype CT scanner with a photon-counting detector (PCD).Approach. MD and CT reconstruction may be done in two successive steps, i.e. decompose the data in material sinograms which are then reconstructed in material CT images, or jointly in a one-step algorithm. The one-step algorithm reconstructed material CT images by maximizing their Poisson log-likelihood in the projection domain with a spatial regularization in the image domain. The two-step algorithm maximized first the Poisson log-likelihood without regularization to decompose the data in material sinograms. These sinograms were then reconstructed into material CT images by least squares minimization, with the same spatial regularization as the one step algorithm. A phantom simulating the CT angiography clinical task was scanned and the data used to measure noise and spatial resolution properties. Low dose carotid CT angiographies of 4 patients were also reconstructed with both algorithms and analyzed by a radiologist. The image quality and diagnostic clinical task were evaluated with a clinical score.Main results. The phantom data processing demonstrated that the one-step algorithm had a better spatial resolution at the same noise level or a decreased noise value at matching spatial resolution. Regularization parameters leading to a fair comparison were selected for the patient data reconstruction. On the patient images, the one-step images received higher scores compared to the two-step algorithm for image quality and diagnostic.Significance. Both phantom and patient data demonstrated how a one-step algorithm improves spectral CT image quality over the implemented two-step algorithm but requires a longer computation time. At a low radiation dose, the one-step algorithm presented good to excellent clinical scores for all the spectral CT images.

MB-DECTNet: a model-based unrolling network for accurate 3D dual-energy CT reconstruction from clinically acquired helical scans

Objective.Over the past several decades, dual-energy CT (DECT) imaging has seen significant advancements due to its ability to distinguish between materials. DECT statistical iterative reconstruction (SIR) has exhibited potential for noise reduction and enhanced accuracy. However, its slow convergence and substantial computational demands render the elapsed time for 3D DECT SIR often clinically unacceptable. The objective of this study is to accelerate 3D DECT SIR while maintaining subpercentage or near-subpercentage accuracy.Approach.We incorporate DECT SIR into a deep-learning model-based unrolling network for 3D DECT reconstruction (MB-DECTNet), which can be trained end-to-end. This deep learning-based approach is designed to learn shortcuts between initial conditions and the stationary points of iterative algorithms while preserving the unbiased estimation property of model-based algorithms. MB-DECTNet comprises multiple stacked update blocks, each containing a data consistency layer (DC) and a spatial mixer layer, with the DC layer functioning as a one-step update from any traditional iterative algorithm.Main results.The quantitative results indicate that our proposed MB-DECTNet surpasses both the traditional image-domain technique (MB-DECTNet reduces average bias by a factor of 10) and a pure deep learning method (MB-DECTNet reduces average bias by a factor of 8.8), offering the potential for accurate attenuation coefficient estimation, akin to traditional statistical algorithms, but with considerably reduced computational costs. This approach achieves 0.13% bias and 1.92% mean absolute error and reconstructs a full image of a head in less than 12 min. Additionally, we show that the MB-DECTNet output can serve as an initializer for DECT SIR, leading to further improvements in results.Significance.This study presents a model-based deep unrolling network for accurate 3D DECT reconstruction, achieving subpercentage error in estimating virtual monoenergetic images for a full head at 60 and 150 keV in 30 min, representing a 40-fold speedup compared to traditional approaches. These findings have significant implications for accelerating DECT SIR and making it more clinically feasible.

Material decomposition using dual-energy CT with unsupervised learning

Material decomposition (MD) is an application of dual-energy computed tomography (DECT) that decomposes DECT images into specific material images. However, the direct inversion method used in MD often amplifies noise in the decomposed material images, resulting in lower image quality. To address this issue, we propose an image-domain MD method based on the concept of deep image prior (DIP). DIP is an unsupervised learning method that can perform different tasks without using a large training dataset with known targets (i.e., basis material images). We retrospectively recruited patients who underwent non-contrast brain DECT scans and investigated the feasibility of using the proposed DIP-based method to decompose DECT images into two (i.e., bone and soft tissue) and three (i.e., bone, soft tissue, and fat) basis materials. We evaluated the decomposed material images in terms of signal-to-noise ratio (SNR) and modulation transfer function (MTF). The proposed DIP-based method showed greater improvement in SNR in the decomposed soft-tissue images compared to the direct inversion method and the iterative method. Moreover, the proposed method produced similar MTF curves in both two- and three-material decompositions. Additionally, the proposed DIP-based method demonstrated better separation ability than the other two studied methods in the case of three-material decomposition. Our results suggest that the proposed DIP-based method is capable of unsupervisedly generating high-quality basis material images from DECT images.

A Locally Weighted Linear Regression Look-Up Table-Based Iterative Reconstruction Method for Dual Spectral CT

OBJECTIVE

Compared with traditional computed tomography (CT), dual spectral CT (DSCT) exhibits superior material distinguishability and thus has broad prospects in industrial and medical fields. In iterative DSCT algorithms, accurately modeling forward-projection functions is crucial, but it is very difficult to analytically provide accurate functions.

METHODS

In this article, we propose a locally weighted linear regression look-up table-based (LWLR-LUT) iterative reconstruction method for DSCT. First, the proposed method uses LWLR to establish LUTs for the forward-projection functions through calibration phantoms, achieving good local information calibration. Second, the reconstructed images can be iteratively obtained through the established LUTs. The proposed method not only does not require knowledge of the X-ray spectra and the attenuation coefficients, but also implicitly accounts for some scattered radiation while fitting locally the forward-projection functions in the calibration space.

RESULTS

Both numerical simulations and real data experiments demonstrate that the proposed method can achieve highly accurate polychromatic forward-projection functions and greatly improve the quality of the images reconstructed from scattering-free and scattering projections.

CONCLUSION

The proposed method is simple and practical, and achieves good material decomposition effects for objects with different complex structures through simple calibration phantoms.

Constrained one-step material decomposition reconstruction of head CT data from a silicon photon-counting prototype

BACKGROUND

Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One-Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantom data.

PURPOSE

This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon-counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large-scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detector effects.

METHODS

Head CT data were acquired on an early prototype clinical PCCT system using an edge-on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two-step projection-domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TVmin ) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two-step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft-tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two-step methods for a range of regularization constraint settings.

RESULTS

cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin , when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVmin algorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft-tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values.

CONCLUSIONS

The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large-scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TVmin two-step approach.

Joint Reconstruction and Spectrum Refinement for Photon-Counting-Detector Spectral CT

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective.Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions.Approach.We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm.Main results.Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term.Significance.We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

Direct Multi-Material Reconstruction via Iterative Proximal Adaptive Descent for Spectral CT Imaging

Spectral computed tomography (spectral CT) is a promising medical imaging technology because of its ability to provide information on material characterization and quantification. However, with an increasing number of basis materials, the nonlinearity of measurements causes difficulty in decomposition. In addition, noise amplification and beam hardening further reduce image quality. Thus, improving the accuracy of material decomposition while suppressing noise is pivotal for spectral CT imaging. This paper proposes a one-step multi-material reconstruction model as well as an iterative proximal adaptive decent method. In this approach, a proximal step and a descent step with adaptive step size are designed under the forward-backward splitting framework. The convergence analysis of the algorithm is further discussed according to the convexity of the optimization objective function. For simulation experiments with different noise levels, the peak signal-to-noise ratio (PSNR) obtained by the proposed method increases approximately 23 dB, 14 dB, and 4 dB compared to those of other algorithms. Magnified areas of thorax data further demonstrated that the proposed method has a better ability to preserve details in tissues, bones, and lungs. Numerical experiments verify that the proposed method efficiently reconstructed the material maps, and reduced noise and beam hardening artifacts compared with the state-of-the-art methods.

Dual- and multi-energy CT for particle stopping-power estimation: current state, challenges and potential

Range uncertainty has been a key factor preventing particle radiotherapy from reaching its full physical potential. One of the main contributing sources is the uncertainty in estimating particle stopping power (ρ_s) within patients. Currently, theρ_sdistribution in a patient is derived from a single-energy CT (SECT) scan acquired for treatment planning by converting CT number expressed in Hounsfield units (HU) of each voxel toρ_susing a Hounsfield look-up table (HLUT), also known as the CT calibration curve. HU andρ_sshare a linear relationship with electron density but differ in their additional dependence on elemental composition through different physical properties, i.e. effective atomic number and mean excitation energy, respectively. Because of that, the HLUT approach is particularly sensitive to differences in elemental composition between real human tissues and tissue surrogates as well as tissue variations within and among individual patients. The use of dual-energy CT (DECT) forρ_sprediction has been shown to be effective in reducing the uncertainty inρ_sestimation compared to SECT. The acquisition of CT data over different x-ray spectra yields additional information on the material elemental composition. Recently, multi-energy CT (MECT) has been explored to deduct material-specific information with higher dimensionality, which has the potential to further improve the accuracy ofρ_sestimation. Even though various DECT and MECT methods have been proposed and evaluated over the years, these approaches are still only scarcely implemented in routine clinical practice. In this topical review, we aim at accelerating this translation process by providing: (1) a comprehensive review of the existing DECT/MECT methods forρ_sestimation with their respective strengths and weaknesses; (2) a general review of uncertainties associated with DECT/MECT methods; (3) a general review of different aspects related to clinical implementation of DECT/MECT methods; (4) other potential advanced DECT/MECT applications beyondρ_sestimation.

Spectral CT reconstruction via low-rank representation and structure preserving regularization

Objective:With the development of computed tomography (CT) imaging technology, it is possible to acquire multi-energy data by spectral CT. Being different from conventional CT, the X-ray energy spectrum of spectral CT is cut into several narrow bins which leads to the result that only a part of photon can be collected in each individual energy channel.This can severely degrade the image qualities. To address this problem, we propose a spectral CT reconstruction algorithm based on low-rank representation and structure preserving regularization in this paper.Approach:To make full use of the prior knowledge about both the inter-channel correlation and the sparsity in gradient domain of inner-channel data, this paper combines a low-rank correlation descriptor with a structure extraction operator as priori regularization terms for spectral CT reconstruction. Furthermore, a split-Bregman based iterative algorithm is developed to solve the reconstruction model. Finally, we propose a multi-channel adaptive parameters generation strategy according to CT values of each individual energy channel.Main results: Experimental results on numerical simulations and real mouse data indicate that the proposed algorithm achieves higher accuracy on both reconstruction and material decomposition than the methods based on simultaneous algebraic reconstruction technique (SART), total variation minimization (TVM), total variation with low-rank (LRTV), and spatial-spectral cube matching frame (SSCMF). Compared with SART, our algorithm improves the feature similarity (FSIM) by 40.4% on average for numerical simulation reconstruction, whereas TVM, LRTV, and SSCMF correspond to 26.1%, 28.2%, and 29.5%, respectively.Significance: We outline a multi-channel reconstruction algorithm tailored for spectral CT. The qualitative and quantitative comparisons present a significant improvement of image quality, indicating its promising potential in spectral CT imaging.

Spectral CT reconstruction via Spectral-Image Tensor and Bidirectional Image-gradient minimization

It is challenging to obtain good image quality in spectral computed tomography (CT) as the photon-number for the photon-counting detectors is limited for each narrow energy bin. This results in a lower signal to noise ratio (SNR) for the projections. To handle this issue, we first formulate the weight bidirectional image gradient with L₀-norm constraint of spectral CT image. Then, as a new regularizer, bidirectional image gradient with L₀-norm constraint is introduced into the tensor decomposition model, generating the Spectral-Image Tensor and Bidirectional Image-gradient Minimization (SITBIM) algorithm. Finally, the split-Bregman method is employed to optimize the proposed SITBIM mathematical model. The experiments on the numerical mouse phantom and real mouse experiments are designed to validate and evaluate the SITBIM method. The results demonstrate that the SITBIM can outperform other state-of-the-art methods (including TVM, TV + LR, SSCMF and NLCTF). INDEX TERMS: -spectral CT, image reconstruction, tensor decomposition, unidirectional image gradient, image similarity.

Spectral CT imaging: Technical principles of dual-energy CT and multi-energy photon-counting CT

Spectral computed tomography (CT) imaging encompasses a unique generation of CT systems based on a simple principle that makes use of the energy-dependent information present in CT images. Over the past two decades this principle has been expanded with the introduction of dual-energy CT systems. The first generation of spectral CT systems, represented either by dual-source or dual-layer technology, opened up a new imaging approach in the radiology community with their ability to overcome the limitations of tissue characterization encountered with conventional CT. Its expansion worldwide can also be considered as an important leverage for the recent groundbreaking technology based on a new chain of detection available on photon counting CT systems, which holds great promise for extending CT towards multi-energy CT imaging. The purpose of this article was to detail the basic principles and techniques of spectral CT with a particular emphasis on the newest technical developments of dual-energy and multi-energy CT systems.

Deep learning-based virtual noncalcium imaging in multiple myeloma using dual-energy CT

BACKGROUND

Dual-energy CT with virtual noncalcium (VNCa) images allows the evaluation of focal intramedullary bone marrow involvement in patients with multiple myeloma. However, current commercial VNCa techniques suffer from excessive image noise and artifacts due to material decomposition used in synthesizing VNCa images.

OBJECTIVES

In this work, we aim to improve VNCa image quality for the assessment of focal multiple myeloma, using an Artificial intelligence based Generalizable Algorithm for mulTi-Energy CT (AGATE) method.

MATERIALS AND METHODS

AGATE method used a custom dual-task convolutional neural network (CNN) that concurrently carries out material classification and quantification. The material classification task provided an auxiliary regularization to the material quantification task. CNN parameters were optimized using custom loss functions that involved cross-entropy, physics-informed constraints, structural redundancy in spectral and material images, and texture information in spectral images. For training data, CT phantoms (diameters 30 to 45 cm) with tissue-mimicking inserts were scanned on a third generation dual-source CT system. Scans were performed at routine dose and half of the routine dose. Small image patches (i.e., 40 × 40 pixels) of tissue-mimicking inserts with known basis material densities were extracted for training samples. Numerically simulated insert materials with various shapes increased diversity of training samples. Generalizability of AGATE was evaluated using CT images from phantoms and patients. In phantoms, material decomposition accuracy was estimated using mean-absolute-percent-error (MAPE), using physical inserts that were not used during the training. Noise power spectrum (NPS) and modulation transfer function (MTF) were compared across phantom sizes and radiation dose levels. Five patients with multiple myeloma underwent dual-energy CT, with VNCa images generated using a commercial method and AGATE. Two fellowship-trained musculoskeletal radiologists reviewed the VNCa images (commercial and AGATE) side-by-side using a dual-monitor display, blinded to VNCa type, rating the image quality for focal multiple myeloma lesion visualization using a 5-level Likert comparison scale (-2 = worse visualization and diagnostic confidence, -1 = worse visualization but equivalent diagnostic confidence, 0 = equivalent visualization and diagnostic confidence, 1 = improved visualization but equivalent diagnostic confidence, 2 = improved visualization and diagnostic confidence). A post hoc assignment of comparison ratings was performed to rank AGATE images in comparison to commercial ones.

RESULTS

AGATE demonstrated consistent material quantification accuracy across phantom sizes and radiation dose levels, with MAPE ranging from 0.7% to 4.4% across all testing materials. Compared to commercial VNCa images, the AGATE-synthesized VNCa images yielded considerably lower image noise (50-77% noise reduction) without compromising noise texture or spatial resolution across different phantom sizes and two radiation doses. AGATE VNCa images had markedly reduced area under NPS curves and maintained NPS peak frequency (0.7 lp/cm to 1.0 lp/cm), with similar MTF curves (50% MTF at 3.0 lp/cm). In patients, AGATE demonstrated reduced image noise and artifacts with improved delineation of focal multiple myeloma lesions (all readers comparison scores indicating improved overall diagnostic image quality [scores 1 or 2]).

CONCLUSIONS

AGATE demonstrated reduced noise and artifacts in VNCa images and ability to improve visualization of bone marrow lesions for assessing multiple myeloma.

Design Optimization of Spatial-Spectral Filters for Cone-Beam CT Material Decomposition

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a one-step direct model-based material decomposition (MBMD) to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This spectral CT performance metric can be used to optimize spectral CT system design. We conducted simulation-based design optimization study to find optimized combinations of filter materials, filter thicknesses, filter widths, and source settings. Finally, we present MBMD results using simulated SSF CT measurements from the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs. Our results indicate that optimizing SSF CT for separability leads to high-performance at material discrimination tasks.

Virtual computed-tomography system for deep-learning-based material decomposition

Objective. Material decomposition (MD) evaluates the elemental composition of human tissues and organs via computed tomography (CT) and is indispensable in correlating anatomical images with functional ones. A major issue in MD is inaccurate elemental information about the real human body. To overcome this problem, we developed a virtual CT system model, by which various reconstructed images can be generated based on ICRP110 human phantoms with information about six major elements (H, C, N, O, P, and Ca). Approach. We generated CT datasets labelled with accurate elemental information using the proposed generative CT model and trained a deep learning (DL)-based model to estimate the material distribution with the ICRP110 based human phantom as well as the digital Shepp–Logan phantom. The accuracy in quad-, dual-, and single-energy CT cases was investigated. The influence of beam-hardening artefacts, noise, and spectrum variations were analysed with testing datasets including elemental density and anatomical shape variations. Main results. The results indicated that this DL approach can realise precise MD, even with single-energy CT images. Moreover, noise, beam-hardening artefacts, and spectrum variations were shown to have minimal impact on the MD. Significance. Present results suggest that the difficulty to prepare a large CT database can be solved by introducing the virtual CT system and the proposed technique can be applied to clinical radiodiagnosis and radiotherapy.

Feasibility study of three-material decomposition in dual-energy cone-beam CT imaging with deep learning

Objective. In this work, a dedicated end-to-end deep convolutional neural network, named as Triple-CBCT, is proposed to demonstrate the feasibility of reconstructing three different material distribution volumes from the dual-energy CBCT projection data. Approach. In Triple-CBCT, the features of the sinogram and the CT image are independently extracted and cascaded via a customized domain transform network module. This Triple-CBCT network was trained by numerically synthesized dual-energy CBCT data, and was tested with experimental dual-energy CBCT data of the Iodine-CaCl2 solution and pig leg specimen scanned on an in-house benchtop system. Main results. Results show that the information stored in both the sinogram and CT image domains can be used together to improve the decomposition quality of multiple materials (water, iodine, CaCl2 or bone) from the dual-energy projections. In addition, both the numerical and experimental results demonstrate that the Triple-CBCT is able to generate high-fidelity dual-energy CBCT basis images. Significance. An innovative end-to-end network that joints the sinogram and CT image domain information is developed to facilitate high quality automatic decomposition from the dual-energy CBCT scans.

Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

Objective. We develop a model-based optimization algorithm for 'one-step' dual-energy (DE) CT decomposition of three materials directly from projection measurements.Approach.Since the three-material problem is inherently undetermined, we incorporate the volume conservation principle (VCP) as a pair of equality and nonnegativity constraints into the objective function of the recently reported model-based material decomposition (MBMD). An optimization algorithm (constrained MBMD, CMBMD) is derived that utilizes voxel-wise separability to partition the volume into a VCP-constrained region solved using interior-point iterations, and an unconstrained region (air surrounding the object, where VCP is violated) solved with conventional two-material MBMD. Constrained MBMD (CMBMD) is validated in simulations and experiments in application to bone composition measurements in the presence of metal hardware using DE cone-beam CT (CBCT). A kV-switching protocol with non-coinciding low- and high-energy (LE and HE) projections was assumed. CMBMD with decomposed base materials of cortical bone, fat, and metal (titanium, Ti) is compared to MBMD with (i) fat-bone and (ii) fat-Ti bases.Main results.Three-material CMBMD exhibits a substantial reduction in metal artifacts relative to the two-material MBMD implementations. The accuracies of cortical bone volume fraction estimates are markedly improved using CMBMD, with ∼5-10× lower normalized root mean squared error in simulations with anthropomorphic knee phantoms (depending on the complexity of the metal component) and ∼2-2.5× lower in an experimental test-bench study.Significance.In conclusion, we demonstrated one-step three-material decomposition of DE CT using volume conservation as an optimization constraint. The proposed method might be applicable to DE applications such as bone marrow edema imaging (fat-bone-water decomposition) or multi-contrast imaging, especially on CT/CBCT systems that do not provide coinciding LE and HE ray paths required for conventional projection-domain DE decomposition.

One-step iterative reconstruction approach based on eigentissue decomposition for spectral photon-counting computed tomography

Purpose: We propose a one-step tissue characterization method for spectral photon-counting computed tomography (SPCCT) using eigentissue decomposition (ETD), tailored for highly accurate human tissue characterization in radiotherapy. Methods: The approach combines a Poisson likelihood, a spatial prior, and a quantitative prior constraining eigentissue fractions based on expected values for tabulated tissues. There are two regularization parameters: α for the quantitative prior, and β for the spatial prior. The approach is validated in a realistic simulation environment for SPCCT. The impact of α and β is evaluated on a virtual phantom. The framework is tested on a virtual patient and compared with two sinogram-based two-step methods [using respectively filtered backprojection (FBP) and an iterative method for the second step] and a post-reconstruction approach with the same quantitative prior. All methods use ETD. Results: Optimal performance with respect to bias or RMSE is achieved with different combinations of α and β on the cylindrical phantom. Evaluated in tissues of the virtual patient, the one-step framework outperforms two-step and post-reconstruction approaches to quantify proton-stopping power (SPR). The mean absolute bias on the SPR is 0.6% (two-step FBP), 0.6% (two-step iterative), 0.6% (post-reconstruction), and 0.2% (one-step optimized for low bias). Following the same order, the RMSE on the SPR is 13.3%, 2.5%, 3.2%, and 1.5%. Conclusions: Accurate and precise characterization with ETD can be achieved with noisy SPCCT data without the need to rely on post-reconstruction methods. The one-step framework is more accurate and precise than two-step methods for human tissue characterization.

An improved iterative neural network for high-quality image-domain material decomposition in dual-energy CT

PURPOSE

Dual-energy computed tomography (DECT) has been widely used in many applications that need material decomposition. Image-domain methods directly decompose material images from high- and low-energy attenuation images, and thus, are susceptible to noise and artifacts on attenuation images. The purpose of this study is to develop an improved iterative neural network (INN) for high-quality image-domain material decomposition in DECT, and to study its properties.

METHODS

We propose a new INN architecture for DECT material decomposition. The proposed INN architecture uses distinct cross-material convolutional neural network (CNN) in image refining modules, and uses image decomposition physics in image reconstruction modules. The distinct cross-material CNN refiners incorporate distinct encoding-decoding filters and cross-material model that captures correlations between different materials. We study the distinct cross-material CNN refiner with patch-based reformulation and tight-frame condition.

RESULTS

Numerical experiments with extended cardiac-torso phantom and clinical data show that the proposed INN significantly improves the image quality over several image-domain material decomposition methods, including a conventional model-based image decomposition (MBID) method using an edge-preserving regularizer, a recent MBID method using pre-learned material-wise sparsifying transforms, and a noniterative deep CNN method. Our study with patch-based reformulations reveals that learned filters of distinct cross-material CNN refiners can approximately satisfy the tight-frame condition.

CONCLUSIONS

The proposed INN architecture achieves high-quality material decompositions using iteration-wise refiners that exploit cross-material properties between different material images with distinct encoding-decoding filters. Our tight-frame study implies that cross-material CNN refiners in the proposed INN architecture are useful for noise suppression and signal restoration. This article is protected by copyright. All rights reserved.

Statistical iterative spectral CT imaging method based on blind separation of polychromatic projections

Spectral computed tomography (CT) can provide narrow-energy-width reconstructed images, thereby suppressing beam hardening artifacts and providing rich attenuation information for component characterization. We propose a statistical iterative spectral CT imaging method based on blind separation of polychromatic projections to improve the accuracy of narrow-energy-width image decomposition. For direct inversion in blind scenarios, we introduce the system matrix into the X-ray multispectral forward model to reduce indirect errors. A constrained optimization problem with edge-preserving regularization is established and decomposed into two sub-problems to be alternately solved. Experiments indicate that the novel algorithm obtains more accurate narrow-energy-width images than the state-of-the-art method.

Addressing CT metal artifacts using photon-counting detectors and one-step spectral CT image reconstruction

PURPOSE

The constrained one-step spectral CT image reconstruction (cOSSCIR) algorithm with a nonconvex alternating direction method of multipliers optimizer is proposed for addressing computed tomography (CT) metal artifacts caused by beam hardening, noise, and photon starvation. The quantitative performance of cOSSCIR is investigated through a series of photon-counting CT simulations.

METHODS

cOSSCIR directly estimates basis material maps from photon-counting data using a physics-based forward model that accounts for beam hardening. The cOSSCIR optimization framework places constraints on the basis maps, which we hypothesize will stabilize the decomposition and reduce streaks caused by noise and photon starvation. Another advantage of cOSSCIR is that the spectral data need not be registered, so that a ray can be used even if some energy window measurements are unavailable. Photon-counting CT acquisitions of a virtual pelvic phantom with low-contrast soft tissue texture and bilateral hip prostheses were simulated. Bone and water basis maps were estimated using the cOSSCIR algorithm and combined to form a virtual monoenergetic image for the evaluation of metal artifacts. The cOSSCIR images were compared to a "two-step" decomposition approach that first estimated basis sinograms using a maximum likelihood algorithm and then reconstructed basis maps using an iterative total variation constrained least-squares optimization (MLE+TVmin $_{\text{min}}$ ). Images were also compared to a nonspectral TVmin $_{\text{min}}$ reconstruction of the total number of counts detected for each ray with and without normalized metal artifact reduction (NMAR) applied. The simulated metal density was increased to investigate the effects of increasing photon starvation. The quantitative error and standard deviation in regions of the phantom were compared across the investigated algorithms. The ability of cOSSCIR to reproduce the soft-tissue texture, while reducing metal artifacts, was quantitatively evaluated.

RESULTS

Noiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TVmin $_{\text{min}}$ algorithms to the correct basis maps in the presence of beam-hardening effects. When noise was simulated, cOSSCIR demonstrated a quantitative error of -1 HU, compared to 2 HU error for the MLE+TVmin $_{\text{min}}$ algorithm and -154 HU error for the nonspectral TVmin $_{\text{min}}$ +NMAR algorithm. For the cOSSCIR algorithm, the standard deviation in the central iodine region of interest was 20 HU, compared to 299 HU for the MLE+TVmin $_{\text{min}}$ algorithm, 41 HU for the MLE+TVmin $_{\text{min}}$ +Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TVmin $_{\text{min}}$ +NMAR algorithm. Increasing levels of photon starvation did not impact the bias or standard deviation of the cOSSCIR images. cOSSCIR was able to reproduce the soft-tissue texture when an appropriate regularization constraint value was selected.

CONCLUSIONS

By directly inverting photon-counting CT data into basis maps using an accurate physics-based forward model and a constrained optimization algorithm, cOSSCIR avoids metal artifacts due to beam hardening, noise, and photon starvation. The cOSSCIR algorithm demonstrated improved stability and accuracy compared to a two-step method of decomposition followed by reconstruction.

Spectral Photon-Counting Computed Tomography: A Review on Technical Principles and Clinical Applications

Photon-counting computed tomography (CT) is a technology that has attracted increasing interest in recent years since, thanks to new-generation detectors, it holds the promise to radically change the clinical use of CT imaging. Photon-counting detectors overcome the major limitations of conventional CT detectors by providing very high spatial resolution without electronic noise, providing a higher contrast-to-noise ratio, and optimizing spectral images. Additionally, photon-counting CT can lead to reduced radiation exposure, reconstruction of higher spatial resolution images, reduction of image artifacts, optimization of the use of contrast agents, and create new opportunities for quantitative imaging. The aim of this review is to briefly explain the technical principles of photon-counting CT and, more extensively, the potential clinical applications of this technology.

Feasibility of Dual-Energy Cone-Beam CT of Bone Marrow Edema Using Dual-Layer Flat Panel Detectors

Purpose

We investigated the feasibility of detection and quantification of bone marrow edema (BME) using dual-energy (DE) Cone-Beam CT (CBCT) with a dual-layer flat panel detector (FPD) and three-material decomposition.

Methods

A realistic CBCT system simulator was applied to study the impact of detector quantization, scatter, and spectral calibration errors on the accuracy of fat-water-bone decompositions of dual-layer projections. The CBCT system featured 975 mm source-axis distance, 1,362 mm source-detector distance and a 430 × 430 mm2 dual-layer FPD (top layer: 0.20 mm CsI:Tl, bottom layer: 0.55 mm CsI:Tl; a 1 mm Cu filter between the layers to improve spectral separation). Tube settings were 120 kV (+2 mm Al, +0.2 mm Cu) and 10 mAs per exposure. The digital phantom consisted of a 160 mm water cylinder with inserts containing mixtures of water (volume fraction ranging 0.18 to 0.46) - fat (0.5 to 0.7) - Ca (0.04 to 0.12); decreasing fractions of fat indicated increasing degrees of BME. A two-stage three-material DE decomposition was applied to DE CBCT projections: first, projection-domain decomposition (PDD) into fat-aluminum basis, followed by CBCT reconstruction of intermediate base images, followed by image-domain change of basis into fat, water and bone. Sensitivity to scatter was evaluated by i) adjusting source collimation (12 to 400 mm width) and ii) subtracting various fractions of the true scatter from the projections at 400 mm collimation. The impact of spectral calibration was studied by shifting the effective beam energy (± 2 keV) when creating the PDD lookup table. We further simulated a realistic BME imaging framework, where the scatter was estimated using a fast Monte Carlo (MC) simulation from a preliminary decomposition of the object; the object was a realistic wrist phantom with an 0.85 mL BME stimulus in the radius.

Results

The decomposition is sensitive to scatter: approx. <20 mm collimation width or <10% error of scatter correction in a full field-of-view setting is needed to resolve BME. A mismatch in PDD decomposition calibration of ± 1 keV results in ~25% error in fat fraction estimates. In the wrist phantom study with MC scatter corrections, we were able to achieve ~0.79 mL true positive and ~0.06 mL false positive BME detection (compared to 0.85 mL true BME volume).

Conclusions

Detection of BME using DE CBCT with dual-layer FPD is feasible, but requires scatter mitigation, accurate scatter estimation, and robust spectral calibration.

Towards sub-percentage uncertainty proton stopping-power mapping via dual-energy CT: direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method

PURPOSE

To assess the potential of a joint dual-energy CT reconstruction process (Statistical Image Reconstruction method built on a Basis Vector Model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial-resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%.

METHODS

JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for ten high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 kVp and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and for our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for 5 different scenarios (comparison of JSIR-BVM SPR/SP to International Commission on Radiation Measurements and Units (ICRU) benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology (JCGM) and the Guide to expression of Uncertainty in Measurement (GUM), including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross-section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method.

RESULTS

Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (Head Phantom) and 1.1% and -1.1% (Body Phantom). The overall RMS deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and two-fold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k = 1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6%-0.9%.

CONCLUSIONS

Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k = 1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial-resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving <1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with sub-percentage accuracy and estimated uncertainty in the clinical setting. This article is protected by copyright. All rights reserved.

One half-scan dual-energy CT imaging using the Dual-domain Dual-way Estimated Network (DoDa-Net) model

BACKGROUND

Compared with single-energy computed tomography (CT), dual-energy CT (DECT) can distinguish materials better. However, most DECT reconstruction theories require two full-scan projection datasets of different energies, and this requirement is hard to meet, especially for cases where a physical blockage disables a full circular rotation. Thus, it is critical to relax the requirements of data acquisition to promote the application of DECT.

METHODS

A flexible one half-scan DECT scheme is proposed, which acquires two projection datasets on two-quarter arcs (one for each energy). The limited-angle problem of the one half-scan DECT scheme can be solved by a reconstruction method. Thus, a dual-domain dual-way estimation network called DoDa-Net is proposed by utilizing the ability of deep learning in non-linear mapping. Specifically, the dual-way mapping Generative Adversarial Network (DM-GAN) was first designed to mine the relationship between two different energy projection data. Two half-scan projection datasets were obtained, the data of which was twice that of the original projection dataset. Furthermore, the data transformation from the projection domain to the image domain was realized by the total variation (TV)-based method. In addition, the image processing network (Im-Net) was employed to optimize the image domain data.

RESULTS

The proposed method was applied to a digital phantom and real anthropomorphic head phantom data to verify its effectiveness. The reconstruction results of the real data are encouraging and prove the proposed method's ability to suppress noise while preserving image details. Also, the experiments conducted on simulated data show that the proposed method obtains the closest results to the ground truth among the comparison methods. For low- and high-energy reconstruction, the peak signal-to-noise ratio (PSNR) of the proposed method is as high as 40.3899 and 40.5573 dB, while the PSNR of other methods is lower than 36.5200 dB. Compared with FBP, TV, and other GAN-based methods, the proposed method reduces root mean square error (RMSE) by, respectively, 0.0124, 0.0037, and 0.0016 for low-energy reconstruction, and 0.0102, 0.0028, and 0.0015 for high-energy reconstruction.

CONCLUSIONS

The developed DoDa-Net model for the proposed one half-scan DECT scheme consists of two stages. In stage one, DM-GAN is used to realize the dual map of projection data. In stage two, the TV-based method is employed to transform the data from the projection domain to the image domain. Furthermore, the reconstructed image is processed by the Im-Net. According to the experimental results of qualitative and quantitative evaluation, the proposed method has advantages in detail preservation, indicating the potential of the proposed method in one half-scan DECT reconstruction.

DIRECT-Net: A unified mutual-domain material decomposition network for quantitative dual-energy CT imaging

PURPOSE

The purpose of this paper is to present an end-to-end deep convolutional neural network to improve the dual-energy CT (DECT) material decomposition performance.

METHODS

In this study, we proposes a unified mutual-domain (sinogram domain and CT domain) material decomposition network (DIRECT-Net) for DECT imaging. By design, the DIRECT-Net has immediate access to mutual-domain data, and utilizes stacked convolution neural network layers for noise reduction and material decomposition. The training data are numerically generated following the fundamental DECT imaging physics. Numerical simulation of the XCAT digital phantom, experiments of a biological specimen, a calcium chloride phantom and an iodine solution phantom are carried out to evaluate the performance of DIRECT-Net. Comparisons are performed with different DECT decomposition algorithms.

RESULTS

Results demonstrate that the proposed DIRECT-Net can generate water and bone basis images with less artifacts compared to the other decomposition methods. Additionally, the quantification errors of the calcium chloride (75-375 mg/cm³ ) and the iodine (2-20 mg/cm³ ) are less than 4%.

CONCLUSIONS

An end-to-end material decomposition network is proposed for quantitative DECT imaging. The qualitative and quantitative results demonstrate that this new DIRECT-Net has promising benefits in improving the DECT image quality.

High-resolution model-based material decomposition in dual-layer flat-panel CBCT

PURPOSE

Spectral CT uses energy-dependent measurements that enable material discrimination in addition to reconstruction of structural information. Flat-panel detectors (FPDs) have been widely used in dedicated and interventional systems to deliver high spatial resolution, volumetric cone-beam CT (CBCT) in compact and OR-friendly designs. In this work, we derive a model-based method that facilitates high-resolution material decomposition in a spectral CBCT system equipped with a prototype dual-layer FPD. Through high-fidelity modeling of multilayer detector, we seek to avoid resolution loss that is present in more traditional processing and decomposition approaches.

METHOD

A physical model for spectral measurements in dual-layer flat-panel CBCT is developed including layer-dependent differences in system geometry, spectral sensitivities, and detector blur (e.g., due to varied scintillator thicknesses). This forward model is integrated into a model-based material decomposition (MBMD) method based on minimization of a penalized weighted least-squared (PWLS) objective function. The noise and resolution performance of this approach was compared with traditional projection-domain decomposition (PDD) and image-domain decomposition (IDD) approaches as well as one-step MBMD with lower-fidelity models that use approximated geometry, projection interpolation, or an idealized system geometry without system blur model. Physical studies using high-resolution three-dimensional (3D)-printed water-iodine phantoms were conducted to demonstrate the high-resolution imaging performance of the compared decomposition methods in iodine basis images and synthetic monoenergetic images.

RESULTS

Physical experiments demonstrate that the MBMD methods incorporating an accurate geometry model can yield higher spatial resolution iodine basis images and synthetic monoenergetic images than PDD and IDD results at the same noise level. MBMD with blur modeling can further improve the spatial-resolution compared with the decomposition results obtained with IDD, PDD, and MBMD methods with lower-fidelity models. Using the MBMD without or with blur model can increase the absolute modulation at 1.75 lp/mm by 10% and 22% compared with IDD at the same noise level.

CONCLUSION

The proposed model-based material decomposition method for a dual-layer flat-panel CBCT system has demonstrated an ability to extend high-resolution performance through sophisticated detector modeling including the layer-dependent blur. The proposed work has the potential to not only facilitate high-resolution spectral CT in interventional and dedicated CBCT systems, but may also provide the opportunity to evaluate different flat-panel design trade-offs including multilayer FPDs with mismatched geometries, scintillator thicknesses, and spectral sensitivities.

Deep learning based spectral CT imaging

Spectral computed tomography (CT) has attracted much attention in radiation dose reduction, metal artifacts removal, tissue quantification and material discrimination. The x-ray energy spectrum is divided into several bins, each energy-bin-specific projection has a low signal-noise-ratio (SNR) than the current-integrating counterpart, which makes image reconstruction a unique challenge. Traditional wisdom is to use prior knowledge based iterative methods. However, this kind of methods demands a great computational cost. Inspired by deep learning, here we first develop a deep learning based reconstruction method; i.e., U-net with L_p^p-norm, Total variation, Residual learning, and Anisotropic adaption (ULTRA). Specifically, we emphasize the various multi-scale feature fusion and multichannel filtering enhancement with a denser connection encoding architecture for residual learning and feature fusion. To address the image deblurring problem associated with the L₂²- loss, we propose a general L_p^p-loss, p>0. Furthermore, the images from different energy bins share similar structures of the same object, the regularization characterizing correlations of different energy bins is incorporated into the L_p^p- loss function, which helps unify the deep learning based methods with traditional compressed sensing based methods. Finally, the anisotropically weighted total variation is employed to characterize the sparsity in the spatial-spectral domain to regularize the proposed network In particular, we validate our ULTRA networks on three large-scale spectral CT datasets, and obtain excellent results relative to the competing algorithms. In conclusion, our quantitative and qualitative results in numerical simulation and preclinical experiments demonstrate that our proposed approach is accurate, efficient and robust for high-quality spectral CT image reconstruction.

An iterative reconstruction method based on monochromatic images for dual energy CT

PURPOSE

Dual-energy computed tomography (DECT) scans objects using two different X-ray spectra to acquire more information, which is also called dual spectral CT (DSCT) in some articles. Compared to traditional CT, DECT exhibits superior material distinguishability. Therefore, DECT can be widely used in the medical and industrial domains. However, owing to the nonlinearity and ill condition of DECT, studies are underway on DECT reconstruction to obtain high quality images and achieve fast convergence speed. Therefore, in this study, we propose an iterative reconstruction method based on monochromatic images (IRM-MI) to rapidly obtain high-quality images in DECT reconstruction.

METHODS

An IRM-MI is proposed for DECT. The proposed method converts DECT reconstruction problem from the basis material images decomposition to monochromatic images decomposition to significantly improve the convergence speed of DECT reconstruction by changing the coefficient matrix of the original equations to increase the angle of the high- and low-energy projection curves or reduce the condition number of the coefficient matrix. The monochromatic images were then decomposed into basis material images. Furthermore, we conducted numerical experiments to evaluate the performance of the proposed method.

RESULTS

The decomposition results of the simulated data and real data experiments confirmed the effectiveness of the proposed method. Compared to the extended algebraic reconstruction technique (E-ART) method, the proposed method exhibited a significant increase in the convergence speed by increasing the angle of polychromatic projection curves or decreasing the condition number of the coefficient matrix, when choosing the appropriate monochromatic images. Therefore, the proposed method is also advantageous in acquiring high quality and rapidly converged images.

CONCLUSIONS

We developed an iterative reconstruction method based on monochromatic images for the material decomposition for DECT. The numerical experiments using the proposed method validated its capability of decomposing the basis material images. Furthermore, the proposed method achieved faster convergence speed compared to the E-ART method.

Invertibility of multi-energy X-ray transform

PURPOSE

The goal is to provide a sufficient condition for the invertibility of a multi-energy (ME) X-ray transform. The energy-dependent X-ray attenuation profiles can be represented by a set of coefficients using the Alvarez-Macovski (AM) method. An ME X-ray transform is a mapping from N AM coefficients to N noise-free energy-weighted measurements, where N ≥ 2 .

METHODS

We apply a general invertibility theorem to prove the equivalence of global and local invertibility for an ME X-ray transform. We explore the global invertibility through testing whether the Jacobian of the mapping J ( A ) has zero values over the support of the mapping. The Jacobian of an arbitrary ME X-ray transform is an integration over all spectral measurements. A sufficient condition for J ( A ) ≠ 0 for all A is that the integrand of J ( A ) is ≥ 0 (or ≤ 0 ) everywhere. Note that the trivial case of the integrand equals 0 everywhere is ignored. Using symmetry, we simplified the integrand of the Jacobian to three factors that are determined by the total attenuation, the basis functions, and the energy-weighting functions, respectively. The factor related to the total attenuation is always positive; hence, the invertibility of the X-ray transform can be determined by testing the signs of the other two factors. Furthermore, we use the Cramér-Rao lower bound (CRLB) to characterize the noise-induced estimation uncertainty and provide a maximum-likelihood (ML) estimator.

RESULTS

The factor related to the basis functions is always negative when the photoelectric/Compton/Rayleigh basis functions are used and K-edge materials are not considered. The sign of the energy-weighting factor depends on the system source spectra and the detector response functions. For four special types of X-ray detectors, the sign of this factor stays the same over the integration range. Therefore, when these four types of detectors are used for imaging non-K-edge materials, the ME X-ray transform is globally invertible. The same framework can be used to study an arbitrary ME X-ray imaging system, for example, when K-edge materials are present. Furthermore, the ML estimator we presented is an unbiased, efficient estimator and can be used for a wide range of scenes.

CONCLUSIONS

We have provided a framework to study the invertibility of an arbitrary ME X-ray transform and proved the global invertibility for four types of systems.

Iterative material decomposition for spectral CT using self-supervised Noise2Noise prior

Compared to conventional computed tomography (CT), spectral CT can provide the capability of material decomposition, which can be used in many clinical diagnosis applications. However, the decomposed images can be very noisy due to the dose limit in CT scanning and the noise magnification of the material decomposition process. To alleviate this situation, we proposed an iterative one-step inversion material decomposition algorithm with a Noise2Noise prior. The algorithm estimated material images directly from projection data and used a Noise2Noise prior for denoising. In contrast to supervised deep learning methods, the designed Noise2Noise prior was built based on self-supervised learning and did not need external data for training. In our method, the data consistency term and the Noise2Noise network were alternatively optimized in the iterative framework, respectively, using a separable quadratic surrogate (SQS) and the Adam algorithm. The proposed iterative algorithm was validated and compared to other methods on simulated spectral CT data, preclinical photon-counting CT data and clinical dual-energy CT data. Quantitative analysis showed that our proposed method performs promisingly on noise suppression and structure detail recovery.

Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.