Comparison of five one-step reconstruction algorithms for spectral CT

Deep learning-based material decomposition of iodine and calcium in mobile photon counting detector CT

Photon-counting detector (PCD)-based computed tomography (CT) offers several advantages over conventional energy-integrating detector-based CT. Among them, the ability to discriminate energy exhibits significant potential for clinical applications because it provides material-specific information. That is, material decomposition (MD) can be achieved through energy discrimination. In this study, deep learning-based material decomposition was performed using live animal data. We propose MD-Unet, which is a deep learning strategy for material decomposition based on an Unet architecture trained with data from three energy bins. To mitigate the data insufficiency, we developed a pretrained model incorporating various simulation data forms and augmentation strategies. Incorporating these approaches into model training results in enhanced precision in material decomposition, thereby enabling the identification of distinct materials at individual pixel locations. The trained network was applied to the acquired animal data to evaluate material decomposition results. Compared with conventional methods, the newly generated MD-Unet demonstrated more accurate material decomposition imaging. Moreover, the network demonstrated an improved material decomposition ability and significantly reduced noise. In addition, they can potentially offer an enhancement level similar to that of a typical contrast agent. This implies that it can acquire images of the same quality with fewer contrast agents administered to patients, thereby demonstrating its significant clinical value.

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.

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.

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.

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.

Photon Counting CT: Technical Principles, Clinical Applications, and Future Prospects

Photon-counting computed tomography (PCCT) is a new technique that utilizes photon-counting detectors to convert individual X-ray photons directly into an electrical signal, which can achieve higher spatial resolution, improved iodine signal, radiation dose reduction, artifact reduction, and multienergy imaging. This review introduces the technical principles of PCCT, and summarizes its first-in-human experience and current applications in clinical settings, and discusses the future prospects of PCCT.

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.

Bicolor K-edge spectral photon-counting CT imaging for the diagnosis of thoracic endoleaks: A dynamic phantom study

PURPOSE

The purpose of this study was to investigate the feasibility of identifying and characterizing the three most common types of endoleaks within a thoracic aorta aneurysm model using bicolor K-edge imaging with a spectral photon-counting computing tomography (SPCCT) system in combination with a biphasic contrast agent injection.

MATERIALS AND METHODS

Three types of thoracic endoleaks (type 1, 2 and 3) were created in a dynamic anthropomorphic thoracic aorta phantom. Protocol consisted in an injection of an iodinated contrast material followed 80 seconds after an injection of a gadolinium-based contrast agent (GBCA). The phantom was scanned using a clinical prototype SPCCT during bicolor phase imaging consisting in an early distribution of GBCA and a late distribution of iodine. Conventional and spectral images were reconstructed for differentiating between the contrast agents and measuring their respective attenuation values and concentrations inside and outside the stent graft.

RESULTS

Conventional images failed to provide specific dynamic imaging contrast agents in the aneurysmal sac and outside the stent graft while spectral images differentiated their specific distribution. In type 1 and 3 thoracic endoleaks, GBCA concentration was measured outside the stent graft at 6.1 ± 3.7 (standard deviation [SD]) mg/mL and 6.0 ± 4.0 (SD) mg/mL, respectively, in favor of an early blood flow. In type 2 thoracic endoleak, iodine was measured outside the stent graft at 24.3 ± 5.5 (SD) mg/mL in favor of a late blood flow in the aneurysmal sac.

CONCLUSION

Bicolor K-edge imaging enabled SPCCT allows a bicolor characterization of thoracic aorta endoleaks in a single acquisition in combination with a biphasic contrast agent injection.

Multi-material spectral photon-counting micro-CT with minimum residual decomposition and self-supervised deep denoising

Spectral micro-CT imaging with direct-detection energy discriminating photon counting detectors having small pixel size (< 100×100 µm²) is mainly hampered by: i) the limited energy resolution of the imaging device due to charge sharing effects and ii) the unavoidable noise amplification in the images resulting from basis material decomposition. In this work, we present a cone-beam micro-CT setup that includes a CdTe photon counting detector implementing a charge summing hardware solution to correct for the charge-sharing issue and an innovative image processing pipeline based on accurate modeling of the spectral response of the imaging system, an improved basis material decomposition (BMD) algorithm named minimum-residual BMD (MR-BMD), and self-supervised deep convolutional denoising. Experimental tomographic projections having a pixel size of 45×45 µm² of a plastinated mouse sample including I, Ba, and Gd small cuvettes were acquired. Results demonstrate the capability of the combined hardware and software tools to sharply discriminate even between materials having their K-Edge separated by a few keV, such as e.g., I and Ba. By evaluating the quality of the reconstructed decomposed images (water, bone, I, Ba, and Gd), the quantitative performances of the spectral system are here assessed and discussed.

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.

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.

Feasibility of dual-energy CBCT by spectral filtration of a dual-focus CNT x-ray source

Cone beam computed tomography (CBCT) is now widely used in dentistry and growing areas of medical imaging. The presence of strong metal artifacts is however a major concern of using CBCT especially in dentistry due to the presence of highly attenuating dental restorations, fixed appliances, and implants. Virtual monoenergetic images (VMIs) synthesized from dual energy CT (DECT) datasets are known to reduce metal artifacts. Although several techniques exist for DECT imaging, they in general come with significantly increased equipment cost and not available in dental clinics. The objectives of this study were to investigate the feasibility of developing a low-cost dual energy CBCT (DE-CBCT) by retrofitting a regular CBCT scanner with a carbon nanotube (CNT) x-ray source with dual focal spots and corresponding low-energy (LE) and high-energy (HE) spectral filters. A testbed with a CNT field emission x-ray source (NuRay Technology, Chang Zhou, China), a flat panel detector (Teledyne, Waterloo, Canada), and a rotating object stage was used for this feasibility study. Two distinct polychromatic x-ray spectra with the mean photon energies of 66.7keV and 86.3keV were produced at a fixed 120kVp x-ray tube voltage by using Al+Au and Al+Sn foils as the respective LE and HE filters attached to the exist window of the x-ray source. The HE filter attenuated the x-ray photons more than the LE filter. The calculated post-object air kerma rate of the HE beam was 31.7% of the LE beam. An anthropomorphic head phantom (RANDO, Nuclear Associates, Hicksville, NY) with metal beads was imaged using the testbed and the images were reconstructed using an iterative volumetric CT reconstruction algorithm. The VMIs were synthesized using an image-domain basis materials decomposition method with energy ranging from 30 to 150keV. The results were compared to the reconstructed images from a single energy clinical dental CBCT scanner (CS9300, Carestream Dental, Atlanta, GA). A significant reduction of the metal artifacts was observed in the VMI images synthesized at high energies compared to those from the same object imaged by the clinical dental CBCT scanner. The ability of the CNT x-ray source to generate the output needed to compensate the reduction of photon flux due to attenuation from the spectral filters and to maintain the CT imaging time was evaluated. The results demonstrated the feasibility of DE-CBCT imaging using the proposed approach. Metal artifact reduction was achieved in VMIs synthesized. The x-ray output needed for the proposed DE-CBCT can be generated by a fixed-anode CNT x-ray source.

A generalized simultaneous algebraic reconstruction technique (GSART) for dual-energy X-ray computed tomography

BACKGROUND

Dual-energy computed tomography (DECT) is a widely used and actively researched imaging modality that can estimate the physical properties of an object more accurately than single-energy CT (SECT). Recently, iterative reconstruction methods called one-step methods have received attention among various approaches since they can resolve the intermingled limitations of the conventional methods. However, the one-step methods typically have expensive computational costs, and their material decomposition performance is largely affected by the accuracy in the spectral coefficients estimation.

OBJECTIVE

In this study, we aim to develop an efficient one-step algorithm that can effectively decompose into the basis material maps and is less sensitive to the accuracy of the spectral coefficients.

METHODS

By use of a new loss function that employs the non-linear forward model and the weighted squared errors, we propose a one-step reconstruction algorithm named generalized simultaneous algebraic reconstruction technique (GSART). The proposed algorithm was compared with the image-domain material decomposition and other existing one-step reconstruction algorithm.

RESULTS

In both simulation and experimental studies, we demonstrated that the proposed algorithm effectively reduced the beam-hardening artifacts thereby increasing the accuracy in the material decomposition.

CONCLUSIONS

The proposed one-step reconstruction for material decomposition in dual-energy CT outperformed the image-domain approach and the existing one-step algorithm. We believe that the proposed method is a practically very useful addition to the material-selective image reconstruction field.

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.

Photon-counting CT via interleaved/gapped spectral channels: Feasibility and imaging performance

PURPOSE

Compared to energy-integration, photon-counting x-ray detection facilitates the spectral channelization (energy binning) in spectral CT and thus offers the opportunity of implementing data acquisition via sophisticated schemes, e.g., gapping or interleaving in spectral channels. In this article, we report our investigation of the performance of material decomposition based spectral imaging in photon-counting CT implemented in such data acquisition schemes, and their comparison with the benchmark scheme and other schemes without spectral gapping or interleaving.

MATERIALS AND METHODS

Using a deliberately designed anthropomorphic head phantom that mimics the intracranial soft tissues and bony structures, a simulation study is carried out with the focus on two-material decomposition-based spectral imaging in photon-counting CT, under both ideal and realistic detector spectral responses. The projection data are acquired in four spectral channels, and then are sorted to implement the schemes of gapping ((ch₁ , ch₃ ); (ch₂ , ch₄ ); (ch₁ , ch₄ )) and interleaving ((ch₁ , ch₃ )+(ch₂ , ch₄ ); (ch₁ , ch₄ )+(ch₂ , ch₃ ); ((ch₁ +ch₃ ), (ch₂ +ch₄ )); ((ch₁ +ch₄ ), (ch₂ +ch₃ ))) in spectral channels, in addition to the benchmark scheme ((ch₁ +ch₂ ), (ch₃ +ch₄ )) and other conventional schemes (ch₁ , ch₂ ), (ch₂ , ch₃ ) and (ch₃ , ch₄ ), where 'ch' denotes channel, '+' denote addition, and (·,·) the operation of material decomposition and image reconstruction. Using the contrast-to-noise ratio between targeted regions of interest as the figure of merit, we study the performance of spectral imaging (material specific and virtual monochromatic) associated with these spectral channelization schemes.

RESULTS

Under ideal detector spectral response, the scheme (ch₁ , ch₄ ) outperforms the benchmark scheme ((ch₁ +ch₂ ), (ch₃ +ch₄ )) and others in gapped and/or interleaved spectral channelization in material specific imaging, while the interleaved scheme (ch₁ , ch₄ )+(ch₂ , ch₃ ) performs the best in virtual monochromatic imaging. Notably, only about half x-ray dose is utilized in the scheme (ch₁ , ch₄ ) for image formation. Under realistic detector spectral response, the difference in imaging performance over all spectral channelization schemes diminishes, along with degradation in each scheme's individual performance. The results suggest that (i) different strategy in spectral channelization may have to be exercised in material specific imaging and virtual monochromatic imaging, respectively, and (ii) the spectral distortion in realistic detector's response due to charge-sharing, Compton scattering and fluorescent escaping should be mitigated as much as possible.

CONCLUSION

The spectral channelization schemes and associated imaging performance reported herein are novel and thus informative to the community, which may further the understanding of physical fundamentals and design principles for material decomposition based spectral imaging in photon-counting CT and other x-ray related imaging modalities. This article is protected by copyright. All rights reserved.

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.

Nonlinear reconstruction of coded spectral X-ray CT based on material decomposition

Coded spectral X-ray computed tomography (CT) based on K-edge filtered illumination is a cost-effective approach to acquire both 3-dimensional structure of objects and their material composition. This approach allows sets of incomplete rays from sparse views or sparse rays with both spatial and spectral encoding to effectively reduce the inspection duration or radiation dose, which is of significance in biological imaging and medical diagnostics. However, reconstruction of spectral CT images from compressed measurements is a nonlinear and ill-posed problem. This paper proposes a material-decomposition-based approach to directly solve the reconstruction problem, without estimating the energy-binned sinograms. This approach assumes that the linear attenuation coefficient map of objects can be decomposed into a few basis materials that are separable in the spectral and space domains. The nonlinear problem is then converted to the reconstruction of the mass density maps of the basis materials. The dimensionality of the optimization variables is thus effectively reduced to overcome the ill-posedness. An alternating minimization scheme is used to solve the reconstruction with regularizations of weighted nuclear norm and total variation. Compared to the state-of-the-art reconstruction method for coded spectral CT, the proposed method can significantly improve the reconstruction quality. It is also capable of reconstructing the spectral CT images at two additional energy bins from the same set of measurements, thus providing more spectral information of the object.

On the conditioning of basis materials and its impact on multimaterial decomposition-based spectral imaging in photon-counting CT

PURPOSE

Material-specific imaging and virtual monochromatic imaging/analysis are the two forms of spectral imaging in CT implemented via either energy-integration or photon-counting data acquisition. Aimed at further understanding the fundamentals and providing guidelines on its design and implementation, we quantitatively investigate the conditioning (sufficiency in dimensionality, well-posedness in basis functions, and matching of K-edge materials) of basis materials and its impact on the performance of spectral imaging in photon-counting CT.

MATERIALS AND METHODS

Initially, singular value decomposition (SVD) is employed to investigate the dimensionality of material space for multimaterial decomposition-based spectral imaging in photon-counting CT over the energy range [18 150] keV. Then, the SVD is extended to study the well-posedness of basis functions, its relationship with the dimensionality of materials to be imaged, and its impact on imaging performance. A number of phantoms are designed to mimic the soft and bony tissues in the head and contrast enhancement materials (iodine and gadolinium). Simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, are carried out to evaluate and verify the proposed approach of conditioning analysis and the relationship between the conditioning of basis materials and the performance of spectral imaging in photon-counting CT.

RESULTS

The preliminary data show that the dimensionality of biological tissues, including both soft and bony tissues, is effectively equal to two. The dimensionality increments with inclusion of K-edge materials into the materials to be imaged. The well-posedness of basis functions depends on the correlation between the functions and impacts the noise in material decomposition substantially, but affects the noise in virtual monochromatic imaging/analysis moderately. If a K-edge material is in the materials to be imaged, the same K-edge material has to be one of the basis materials, but its concentration does not affect the accuracy of material decomposition significantly. Moreover, inclusion of K-edge material into the basis material makes the tuning of correlation among the basis functions feasible and thus improves the performance of spectral imaging in photon-counting CT.

CONCLUSION

The extension of SVD for systematic analysis of multimaterial decomposition-based spectral imaging in photon-counting CT is of innovation and significance. In addition to providing more information on the fundamentals, the approach used in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in either photon-counting or energy-integration CT, as well as other x-ray-related imaging modalities such as radiography and tomosynthesis.

Quantitative Reconstruction of Polychromatic X-ray Fluorescence Computed Tomography Using Transmission Tomography

Through measuring the intensity of the fluorescence X-rays emitted by the elements of interest, X-ray fluorescence computed tomography (XFCT) is capable of mapping the elemental distribution inside an object without destructively sectioning it. With the recent advances in XFCT utilizing polychromatic microfocus X-ray sources, it is expected that the popularity of such imaging modality will rise further. However, XFCT suffers from self-absorption effects, which make it challenging to reconstruct the elemental distribution inside the sample accurately. For this reason, polychromatic XFCT is mainly used to retrieve the distribution of elements with a relatively high atomic number (Z) when compared to the matrix of the sample. To enable the quantitative reconstruction of trace and low Z elements with polychromatic XFCT, a novel reconstruction method has been proposed in this manuscript. Through examining the proposed method on both simulation data and experimental data, its capacity on retrieving the density distribution of relatively low Z elements has been confirmed.

Photon-counting x-ray detectors for CT

The introduction of photon-counting detectors is expected to be the next major breakthrough in clinical x-ray computed tomography (CT). During the last decade, there has been considerable research activity in the field of photon-counting CT, in terms of both hardware development and theoretical understanding of the factors affecting image quality. In this article, we review the recent progress in this field with the intent of highlighting the relationship between detector design considerations and the resulting image quality. We discuss detector design choices such as converter material, pixel size, and readout electronics design, and then elucidate their impact on detector performance in terms of dose efficiency, spatial resolution, and energy resolution. Furthermore, we give an overview of data processing, reconstruction methods and metrics of imaging performance; outline clinical applications; and discuss potential future developments.

Non-convex primal-dual algorithm for image reconstruction in spectral CT

The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization program, and develop a non-convex primal-dual (NCPD) algorithm to solve the program. We devise multiple convergence conditions and perform verification studies numerically to demonstrate that the NCPD algorithm can solve the non-convex optimization program and under appropriate data condition, can invert the non-linear data model. Using the NCPD algorithm, we then reconstruct monochromatic images from simulated and real data of numerical and physical phantoms acquired with a standard, full-scan dual-energy configuration. The result of the reconstruction studies shows that the NCPD algorithm can correct accurately for the non-linear beam-hardening effect. Furthermore, we apply the NCPD algorithm to simulated and real data of the numerical and physical phantoms collected with non-standard, short-scan dual-energy configurations, and obtain monochromatic images comparable to those of the standard, full-scan study, thus revealing the potential of the NCPD algorithm for enabling non-standard scanning configurations in spectral CT, where the existing indirect methods are limited.

Dual source hybrid spectral micro-CT using an energy-integrating and a photon-counting detector

Preclinical micro-CT provides a hotbed in which to develop new imaging technologies, including spectral CT using photon counting detector (PCD) technology. Spectral imaging using PCDs promises to expand x-ray CT as a functional imaging modality, capable of molecular imaging, while maintaining CT's role as a powerful anatomical imaging modality. However, the utility of PCDs suffers due to distorted spectral measurements, affecting the accuracy of material decomposition. We attempt to improve material decomposition accuracy using our novel hybrid dual-source micro-CT system which combines a PCD and an energy integrating detector. Comparisons are made between PCD-only and hybrid CT results, both reconstructed with our iterative, multi-channel algorithm based on the split Bregman method and regularized with rank-sparse kernel regression. Multi-material decomposition is performed post-reconstruction for separation of iodine (I), gold (Au), gadolinium (Gd), and calcium (Ca). System performance is evaluated first in simulations, then in micro-CT phantoms, and finally in an in vivo experiment with a genetically modified p53fl/fl mouse cancer model with Au, Gd, and I nanoparticle (NP)-based contrasts agents. Our results show that the PCD-only and hybrid CT reconstructions offered very similar spatial resolution at 10% MTF (PCD: 3.50 lp mm-1; hybrid: 3.47 lp mm-1) and noise characteristics given by the noise power spectrum. For material decomposition we note successful separation of the four basis materials. We found that hybrid reconstruction reduces RMSE by an average of 37% across all material maps when compared to PCD-only of similar dose but does not provide much difference in terms of concentration accuracy. The in vivo results show separation of targeted Au and accumulated Gd NPs in the tumor from intravascular iodine NPs and bone. Hybrid spectral micro-CT can benefit nanotechnology and cancer research by providing quantitative imaging to test and optimize various NPs for diagnostic and therapeutic applications.

Spectral photon-counting CT imaging of colorectal peritoneal metastases: initial experience in rats

Computed tomography imaging plays a major role in the preoperative assessment of tumor burden by providing an accurate mapping of the distribution of peritoneal metastases (PM). Spectral Photon Counting Computed Tomography (SPCCT) is an innovative imaging modality that could overcome the current limitations of conventional CT, offering not only better spatial resolution but also better contrast resolution by allowing the discrimination of multiple contrast agents. Based on this capability, we tested the feasibility of SPCCT in the detection of PM at different time of tumor growth in 16 rats inoculated with CC531 cells using dual-contrast injection protocols in two compartments (i.e. intravenous iodine and intraperitoneal gadolinium or the reverse protocol), compared to surgery. For all peritoneal regions and for both protocols, sensitivity was 69%, specificity was 100% and accuracy was 80%, and the correlation with surgical exploration was strong (p = 0.97; p = 0.0001). No significant difference was found in terms of diagnostic performance, quality of peritoneal opacification or diagnostic quality between the 2 injection protocols. We also showed poor vascularization of peritoneal metastases by measuring low concentrations of contrast agent in the largest lesions using SPCCT, which was confirmed by immunohistochemical analyses. In conclusion, SPCCT using dual-contrast agent injection protocols in 2 compartments is a promising imaging modality to assess the extent of PM in a rat model.

Spectral CT imaging method based on blind separation of polychromatic projections with Poisson prior

The linear reconstruction of narrow-energy-width projections can suppress hardening artifacts in conventional computed tomography (CT). We develop a spectral CT blind separation algorithm for obtaining narrow-energy-width projections under a blind scenario where the incident spectra are unknown. The algorithm relies on an X-ray multispectral forward model. Based on the Poisson statistical properties of measurements, a constrained optimization problem is established and solved by a block coordinate descent algorithm that alternates between nonnegative matrix factorization and Gauss-Newton algorithm. Experiments indicate that the decomposed projections conform to the characteristics of narrow-energy-width projections. The new algorithm improves the accuracy of obtaining narrow-energy-width projections.

Multicolor spectral photon counting CT monitors and quantifies therapeutic cells and their encapsulating scaffold in a model of brain damage

Rationale & aim: Various types of cell therapies are currently under investigation for the treatment of ischemic stroke patients. To bridge the gap between cell administration and therapeutic outcome, there is a need for non-invasive monitoring of these innovative therapeutic approaches. Spectral photon counting computed tomography (SPCCT) is a new imaging modality that may be suitable for cell tracking. SPCCT is the next generation of clinical CT that allows the selective visualization and quantification of multiple contrast agents. The aims of this study are: (i) to demonstrate the feasibility of using SPCCT to longitudinally monitor and quantify therapeutic cells, i.e. bone marrow-derived M2-polarized macrophages transplanted in rats with brain damage; and (ii) to evaluate the potential of this approach to discriminate M2-polarized macrophages from their encapsulating scaffold. Methods: Twenty one rats received an intralesional transplantation of bone marrow-derived M2-polarized macrophages. In the first set of experiments, cells were labeled with gold nanoparticles and tracked for up to two weeks post-injection in a monocolor study via gold K-edge imaging. In the second set of experiments, the same protocol was repeated for a bicolor study, in which the labeled cells are embedded in iodine nanoparticle-labeled scaffold. The amount of gold in the brain was longitudinally quantified using gold K-edge images reconstructed from SPCCT acquisition. Animals were sacrificed at different time points post-injection, and ICP-OES was used to validate the accuracy of gold quantification from SPCCT imaging. Results: The feasibility of therapeutic cell tracking was successfully demonstrated in brain-damaged rats with SPCCT imaging. The imaging modality enabled cell monitoring for up to 2 weeks post-injection, in a specific and quantitative manner. Differentiation of labeled cells and their embedding scaffold was also feasible with SPCCT imaging, with a detection limit as low as 5,000 cells in a voxel of 250 × 250 × 250 µm in dimension in vivo. Conclusion: Multicolor SPCCT is an innovative translational imaging tool that allows monitoring and quantification of therapeutic cells and their encapsulating scaffold transplanted in the damaged rat brain.

Feasibility of improving vascular imaging in the presence of metallic stents using spectral photon counting CT and K-edge imaging

Correct visualization of the vascular lumen is impaired in standard computed tomography (CT) because of blooming artifacts, increase of apparent size, induced by metallic stents and vascular calcifications. Recently, due to the introduction of photon-counting detectors in the X-ray imaging field, a new prototype spectral photon-counting CT (SPCCT) based on a modified clinical CT system has been tested in a feasibility study for improving vascular lumen delineation and visualization of coronary stent architecture. Coronary stents of different metal composition were deployed inside plastic tubes containing hydroxyapatite spheres to simulate vascular calcifications and in the abdominal aorta of one New Zealand White (NZW) rabbit. Imaging was performed with an SPCCT prototype, a dual-energy CT system, and a conventional 64-channel CT system (B64). We found the apparent widths of the stents significantly smaller on SPCCT than on the other two systems in vitro (p < 0.01), thus closer to the true size. Consequently, the intra-stent lumen was significantly larger on SPCCT (p < 0.01). In conclusion, owing to the increased spatial resolution of SPCCT, improved lumen visualization and delineation of stent metallic mesh is possible compared to dual-energy and conventional CT.

Feasibility of multi-contrast imaging on dual-source photon counting detector (PCD) CT: An initial phantom study

PURPOSE

Photon-counting-detector-computed tomography (PCD-CT) allows separation of multiple, simultaneously imaged contrast agents, such as iodine (I), gadolinium (Gd), and bismuth (Bi). However, PCDs suffer from several technical limitations such as charge sharing, K-edge escape, and pulse pile-up, which compromise spectral separation of multi-energy data and degrade multi-contrast imaging performance. The purpose of this work was to determine the performance of a dual-source (DS) PCD-CT relative to a single-source (SS) PCD-CT for the separation of simultaneously imaged I, Gd, and Bi contrast agents.

METHODS

Phantom experiments were performed using a research whole-body PCD-CT and head/abdomen-sized phantoms containing vials of different I, Gd, Bi concentrations. To emulate a DS-PCD-CT, the phantoms were scanned twice on the SS-PCD-CT using different tube potentials for each scan. A tube potential of 80 kV (energy thresholds = 25/50 keV) was used for low-energy tube, while the high-energy tube used Sn140 kV (Sn indicates tin filter) and thresholds of 25/90 keV. The same phantoms were scanned also on the SS-PCD-CT using the chess acquisition mode. In chess mode, the 4 × 4 subpixels within a macro detector pixel are split into two sets based on a chess-board pattern. With each subpixel set having two energy thresholds, chess mode allows four energy-bin data sets, which permits simultaneous multi-contrast imaging. Because of this design, only 50% area of each detector pixel is configured to receive photons of a pre-defined threshold, leading to 50% dose utilization efficiency. To compensate for this dose inefficiency, the radiation dose for this scan was doubled compared to DS-PCD-CT. A 140 kV tube potential and thresholds = 25/50/75/90 keV were used. These settings were determined based on the K-edges of Gd, and Bi, and were found to yield good differentiation of I/Gd/Bi based on phantom experiments and other literature. The energy-bin images obtained from each scan (scan pair) were used to generate I-, Gd-, Bi-specific image via material decomposition. Root-mean-square-error (RMSE) between the known and measured concentrations was calculated for each scenario. A 20-cm water cylinder phantom was scanned on both systems, which was used for evaluating the magnitude of noise, and noise power spectra (NPS) of I/Gd/Bi-specific images.

RESULTS

Phantom results showed that DS-PCD-CT reduced noise in material-specific images for both head and body phantoms compared to SS-PCD-CT. The noise level of SS-PCD was reduced from 2.55 to 0.90 mg/mL (I), 1.97 to 0.78 mg/mL (Gd), and 0.85 to 0.74 mg/mL (Bi) using DS-PCD. NPS analysis showed that the noise texture of images acquired on both systems is similar. For the body phantom, the RMSE for SS-PCD-CT was reduced relative to DS-PCD-CT from 10.52 to 2.76 mg/mL (I), 7.90 to 2.01 mg/mL (Gd), and 1.91 to 1.16 mg/mL (Bi). A similar trend was observed for the head phantom: RMSE reduced from 2.59 (SS-PCD) to 0.72 (DS-PCD) mg/mL (I), 2.02 to 0.58 mg/mL (Gd), and 0.85 to 0.57 mg/mL (Bi).

CONCLUSION

We demonstrate the feasibility of performing simultaneous imaging of I, Gd, and Bi materials on DS-PCD-CT. Under the condition without cross scattering, DS-PCD reduced the RMSE for quantification of material concentration in relative to a SS-PCD-CT system using chess mode.

Spectral Photon-Counting Computed Tomography (SPCCT): in-vivo single-acquisition multi-phase liver imaging with a dual contrast agent protocol

Diagnostic imaging of hepatocellular carcinoma (HCC) requires a liver CT or MRI multiphase acquisition protocol. Patients would benefit from a high-resolution imaging method capable of performing multi-phase imaging in a single acquisition without an increase in radiation dose. Spectral Photon-Counting Computed Tomography (SPCCT) has recently emerged as a novel and promising imaging modality in the field of diagnostic radiology. SPCCT is able to distinguish between two contrast agents referred to as multicolor imaging because, when measuring in three or more energy regimes, it can detect and quantify elements with a K-edge in the diagnostic energy range. Based on this capability, we tested the feasibility of a dual-contrast multi-phase liver imaging protocol via the use of iodinated and gadolinated contrast agents on four healthy New Zealand White (NZW) rabbits. To perform a dual-contrast protocol, we injected the agents at different times so that the first contrast agent visualized the portal phase and the second the arterial phase, both of which are mandatory for liver lesion characterization. We demonstrated a sensitive discrimination and quantification of gadolinium within the arteries and iodine within the liver parenchyma. In the hepatic artery, the concentration of gadolinium was much higher than iodine (8.5 ± 3.9 mg/mL versus 0.7 ± 0.1 mg/mL) contrary to the concentrations found in the liver parenchyma (0.5 ± 0.3 mg/mL versus 4.2 ± 0.3 mg/mL). In conclusion, our results confirm that SPCCT allows in-vivo dual contrast qualitative and quantitative multi-phase liver imaging in a single acquisition.

The evolution of image reconstruction for CT-from filtered back projection to artificial intelligence

Abstract

The first CT scanners in the early 1970s already used iterative reconstruction algorithms; however, lack of computational power prevented their clinical use. In fact, it took until 2009 for the first iterative reconstruction algorithms to come commercially available and replace conventional filtered back projection. Since then, this technique has caused a true hype in the field of radiology. Within a few years, all major CT vendors introduced iterative reconstruction algorithms for clinical routine, which evolved rapidly into increasingly advanced reconstruction algorithms. The complexity of algorithms ranges from hybrid-, model-based to fully iterative algorithms. As a result, the number of scientific publications on this topic has skyrocketed over the last decade. But what exactly has this technology brought us so far? And what can we expect from future hardware as well as software developments, such as photon-counting CT and artificial intelligence? This paper will try answer those questions by taking a concise look at the overall evolution of CT image reconstruction and its clinical implementations. Subsequently, we will give a prospect towards future developments in this domain.

Key Points

• Advanced CT reconstruction methods are indispensable in the current clinical setting.

• IR is essential for photon-counting CT, phase-contrast CT, and dark-field CT.

• Artificial intelligence will potentially further increase the performance of reconstruction methods.