TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

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.

MISD-IR: material-image subspace decomposition-based iterative reconstruction with spectrum estimation for dual-energy computed tomography

Background

Dual-energy computed tomography (DECT) is a promising technique, which can provide unique capability for material quantification. The iterative reconstruction of material maps requires spectral information and its accuracy is affected by spectral mismatch. Simultaneously estimating the spectra and reconstructing material maps avoids extra workload on spectrum estimation and the negative impact of spectral mismatch. However, existing methods are not satisfactory in image detail preservation, edge retention, and convergence rate. The purpose of this paper was to mine the similarity between the reconstructed images and the material images to improve the imaging quality, and to design an effective iteration strategy to improve the convergence efficiency.

Methods

The material-image subspace decomposition-based iterative reconstruction (MISD-IR) with spectrum estimation was proposed for DECT. MISD-IR is an optimized model combining spectral estimation and material reconstruction with fast convergence speed and promising noise suppression capability. We proposed to reconstruct the material maps based on extended simultaneous algebraic reconstruction techniques and estimation of the spectrum with model spectral. To stabilize the iteration and alleviate the influence of errors, we introduced a weighted proximal operator based on the block coordinate descending algorithm (WP-BCD). Furthermore, the reconstructed computed tomography (CT) images were introduced to suppress the noise based on subspace decomposition, which relies on non-local regularization to prevent noise accumulation.

Results

In numerical experiments, the results of MISD-IR were closer to the ground truth compared with other methods. In real scanning data experiments, the results of MISD-IR showed sharper edges and details. Compared with other one-step iterative methods in the experiment, the running time of MISD-IR was reduced by 75%.

Conclusions

The proposed MISD-IR can achieve accurate material decomposition (MD) without known energy spectrum in advance, and has good retention of image edges and details. Compared with other one-step iterative methods, it has high convergence efficiency.

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.

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.

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.

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.

Dictionary learning based image-domain material decomposition for spectral CT

The potential huge advantage of spectral computed tomography (CT) is that it can provide accurate material identification and quantitative tissue information by material decomposition. However, material decomposition is a typical inverse problem, where the noise can be magnified. To address this issue, we develop a dictionary learning based image-domain material decomposition (DLIMD) method for spectral CT to achieve accurate material components with better image quality. Specifically, a set of image patches are extracted from the mode-1 unfolding of normalized material images decomposed by direct inversion to train a unified dictionary using the K-SVD technique. Then, the DLIMD model is established to explore the redundant similarities of the material images, where the split-Bregman is employed to optimize the model. Finally, more constraints (i.e. volume conservation and the bounds of each pixel within material maps) are integrated into the DLIMD model. Numerical phantom, physical phantom and preclinical experiments are performed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.

Full-Spectrum-Knowledge-Aware Tensor Model for Energy-Resolved CT Iterative Reconstruction

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a F ull- S pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

Statistical image-based material decomposition for triple-energy computed tomography using total variation regularization

BACKGROUND

Triple-energy computed tomography (TECT) can obtain x-ray attenuation measurements at three energy spectra, thereby allowing identification of different material compositions with same or very similar attenuation coefficients. This ability is known as material decomposition, which can decompose TECT images into different basis material image. However, the basis material image would be severely degraded when material decomposition is directly performed on the noisy TECT measurements using a matrix inversion method.

OBJECTIVE

To achieve high quality basis material image, we present a statistical image-based material decomposition method for TECT, which uses the penalized weighted least-squares (PWLS) criteria with total variation (TV) regularization (PWLS-TV).

METHODS

The weighted least-squares term involves the noise statistical properties of the material decomposition process, and the TV regularization penalizes differences between local neighboring pixels in a decomposed image, thereby contributing to improving the quality of the basis material image. Subsequently, an alternating optimization method is used to minimize the objective function.

RESULTS

The performance of PWLS-TV is quantitatively evaluated using digital and mouse thorax phantoms. The experimental results show that PWLS-TV material decomposition method can greatly improve the quality of decomposed basis material image compared to the quality of images obtained using the competing methods in terms of suppressing noise and preserving edge and fine structure details.

CONCLUSIONS

The PWLS-TV method can simultaneously perform noise reduction and material decomposition in one iterative step, and it results in a considerable improvement of basis material image quality.

Block matching frame based material reconstruction for spectral CT

Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step material reconstruction model based on Taylor's first-order expansion. Then, we develop a basic material reconstruction method named material simultaneous algebraic reconstruction technique (MSART). Considering the local similarity of each material image, we incorporate a powerful block matching frame (BMF) into the material reconstruction (MR) model and generate a BMF based MR (BMFMR) method. Because the BMFMR model contains the L 0-norm problem, we adopt a split-Bregman method for optimization. The numerical simulation and physical phantom experiment results validate the correctness of the material reconstruction algorithms and demonstrate that the BMF regularization outperforms the total variation and no-local mean regularizations.

Photon-counting Detector CT: System Design and Clinical Applications of an Emerging Technology

Photon-counting detector (PCD) CT is an emerging technology that has shown tremendous progress in the last decade. Various types of PCD CT systems have been developed to investigate the benefits of this technology, which include reduced electronic noise, increased contrast-to-noise ratio with iodinated contrast material and radiation dose efficiency, reduced beam-hardening and metal artifacts, extremely high spatial resolution (33 line pairs per centimeter), simultaneous multienergy data acquisition, and the ability to image with and differentiate among multiple CT contrast agents. PCD technology is described and compared with conventional CT detector technology. With the use of a whole-body research PCD CT system as an example, PCD technology and its use for in vivo high-spatial-resolution multienergy CT imaging is discussed. The potential clinical applications, diagnostic benefits, and challenges associated with this technology are then discussed, and examples with phantom, animal, and patient studies are provided. ©RSNA, 2019.

Multi-energy computed tomography reconstruction using a nonlocal spectral similarity model

Multi-energy computed tomography (MECT) is able to acquire simultaneous multi-energy measurements from one scan. In addition, it allows material differentiation and quantification effectively. However, due to the limited energy bin width, the number of photons detected in an energy-specific channel is smaller than that in traditional CT, which results in image quality degradation. To address this issue, in this work, we develop a statistical iterative reconstruction algorithm to acquire high-quality MECT images and high-accuracy material-specific images. Specifically, this algorithm fully incorporates redundant self-similarities within nonlocal regions in the MECT image at one bin and rich spectral similarities among MECT images at all bins. For simplicity, the presented algorithm is referred to as 'MECT-NSS'. Moreover, an efficient optimization algorithm is developed to solve the MECT-NSS objective function. Then, a comprehensive evaluation of parameter selection for the MECT-NSS algorithm is conducted. In the experiment, the datasets include images from three phantoms and one patient to validate and evaluate the MECT-NSS reconstruction performance. The qualitative and quantitative results demonstrate that the presented MECT-NSS can successfully yield better MECT image quality and more accurate material estimation than the competing algorithms.

Image-domain multimaterial decomposition for dual-energy CT based on prior information of material images

PURPOSE

Dual-Energy Computed Tomography (DECT) is of great interest in medical imaging, security inspection, and nondestructive testing. Most DECT reconstruction methods focus on producing two material images with different linear attenuation coefficients. However, the ability to reconstruct three or more basis materials is clinically and industrially important. Under the assumption that there are at most three materials in each pixel, there are a few methods that estimate multiple material images from DECT measurements by enforcing sum-to-one and a box constraint ([0 1]) derived from both the volume and mass conservation assumption. The recently proposed image-domain multimaterial decomposition (MMD) method introduces edge-preserving regularization for each material image. It enforces the assumption that there are at most three materials in each pixel using a time-consuming loop over all possible material triplets. However, this method neglects relations among material images. We propose a new image-domain MMD model for DECT that considers the prior information that different material images have common or complementary edges and encourages sparsity of material composition in each pixel using regularization.

METHOD

The proposed PWLS-TNV-ℓ0 method uses penalized weighted least-square (PWLS) reconstruction with three regularization terms. The first term is total nuclear variation (TNV) that accounts for the image property that basis material images share common or complementary boundaries and each material image is piecewise constant. The second term is an ℓ0 norm that encourages each pixel containing a small subset of material types out of several possible materials. The third term is a characteristic function based on sum-to-one and a box constraint derived from the volume and mass conservation assumption. We apply the Alternating Direction Method of Multipliers (ADMM) to optimize the cost function of the PWLS-TNV-ℓ0 method.

RESULT

We evaluated the proposed method on a simulated digital phantom, Catphan©600 phantom and patient's pelvis data. We implemented two existing image-domain MMD methods for DECT, the Direct Inversion and the PWLS-EP-LOOP method. We initialized the PWLS-TNV-ℓ0 method and the PWLS-EP-LOOP method with the results of the Direct Inversion method and compared performance of the proposed method with that of the PWLS-EP-LOOP method. The proposed method lowers the bias of decomposed material fractions by 84.47% in the digital phantom study, by 99.50% in the Catphan©600 phantom study, and by 99.64% in the pelvis patient study, respectively, compared to the PWLS-EP-LOOP method. The proposed method reduces noise standard deviation (STD) by 52.21% in the Catphan©600 phantom study, and by 16.74% in the patient's pelvis study, compared to the PWLS-EP-LOOP method. The proposed method increases volume fraction accuracy by 6.04%,20.55%, and 13.46% for the digital phantom, the Catphan©600 phantom, and the patient's pelvis study, respectively, compared to the PWLS-EP-LOOP method. Compared with the PWLS-EP-LOOP method, the root mean square percentage error [RMSE(%)] of electron densities in the Catphan©600 phantom is decreased by about 7.39%.

CONCLUSIONS

We proposed an image-domain MMD method, PWLS-TNV-ℓ0 , for DECT. The PWLS-TNV-ℓ0 method takes low rank property of material image gradients, sparsity of material composition and mass and volume conservation into consideration. The proposed method suppresses noise, reduces cross contamination, and improves accuracy in the decomposed material images, compared to the PWLS-EP-LOOP method.

Principal component reconstruction (PCR) for cine CBCT with motion learning from 2D fluoroscopy

PURPOSE

This work aims to generate cine CT images (i.e., 4D images with high-temporal resolution) based on a novel principal component reconstruction (PCR) technique with motion learning from 2D fluoroscopic training images.

METHODS

In the proposed PCR method, the matrix factorization is utilized as an explicit low-rank regularization of 4D images that are represented as a product of spatial principal components and temporal motion coefficients. The key hypothesis of PCR is that temporal coefficients from 4D images can be reasonably approximated by temporal coefficients learned from 2D fluoroscopic training projections. For this purpose, we can acquire fluoroscopic training projections for a few breathing periods at fixed gantry angles that are free from geometric distortion due to gantry rotation, that is, fluoroscopy-based motion learning. Such training projections can provide an effective characterization of the breathing motion. The temporal coefficients can be extracted from these training projections and used as priors for PCR, even though principal components from training projections are certainly not the same for these 4D images to be reconstructed. For this purpose, training data are synchronized with reconstruction data using identical real-time breathing position intervals for projection binning. In terms of image reconstruction, with a priori temporal coefficients, the data fidelity for PCR changes from nonlinear to linear, and consequently, the PCR method is robust and can be solved efficiently. PCR is formulated as a convex optimization problem with the sum of linear data fidelity with respect to spatial principal components and spatiotemporal total variation regularization imposed on 4D image phases. The solution algorithm of PCR is developed based on alternating direction method of multipliers.

RESULTS

The implementation is fully parallelized on GPU with NVIDIA CUDA toolbox and each reconstruction takes about a few minutes. The proposed PCR method is validated and compared with a state-of-art method, that is, PICCS, using both simulation and experimental data with the on-board cone-beam CT setting. The results demonstrated the feasibility of PCR for cine CBCT and significantly improved reconstruction quality of PCR from PICCS for cine CBCT.

CONCLUSION

With a priori estimated temporal motion coefficients using fluoroscopic training projections, the PCR method can accurately reconstruct spatial principal components, and then generate cine CT images as a product of temporal motion coefficients and spatial principal components.

A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images (<1% error). In experiments, the proposed method estimated the low-density polyethylene region of the basis maps with 0.5% error in the PMMA image and 4% error in the aluminum image. For the Teflon region, the experimental results demonstrated 8% and 31% error in the PMMA and aluminum basis material maps, respectively, compared with -24% and 126% error without estimation of the effective energy window spectra, with residual errors likely due to insufficient modeling of detector effects. The cOSSCIR algorithm estimated the material decomposition angle to within 1.3 degree error, where, for reference, the difference in angle between PMMA and muscle tissue is 2.1 degrees. The joint estimation of spectral-response scaling coefficients and basis material maps was found to reduce ring artifacts in both a phantom and tissue specimen. The presented validation procedure demonstrated feasibility for the automated determination of algorithm constraint parameters.

Low-dose 4D cone-beam CT via joint spatiotemporal regularization of tensor framelet and nonlocal total variation

Excessive radiation exposure is still a major concern in 4D cone-beam computed tomography (4D-CBCT) due to its prolonged scanning duration. Radiation dose can be effectively reduced by either under-sampling the x-ray projections or reducing the x-ray flux. However, 4D-CBCT reconstruction under such low-dose protocols is prone to image artifacts and noise. In this work, we propose a novel joint regularization-based iterative reconstruction method for low-dose 4D-CBCT. To tackle the under-sampling problem, we employ spatiotemporal tensor framelet (STF) regularization to take advantage of the spatiotemporal coherence of the patient anatomy in 4D images. To simultaneously suppress the image noise caused by photon starvation, we also incorporate spatiotemporal nonlocal total variation (SNTV) regularization to make use of the nonlocal self-recursiveness of anatomical structures in the spatial and temporal domains. Under the joint STF-SNTV regularization, the proposed iterative reconstruction approach is evaluated first using two digital phantoms and then using physical experiment data in the low-dose context of both under-sampled and noisy projections. Compared with existing approaches via either STF or SNTV regularization alone, the presented hybrid approach achieves improved image quality, and is particularly effective for the reconstruction of low-dose 4D-CBCT data that are not only sparse but noisy.

Iterative reconstruction for dual energy CT with an average image-induced nonlocal means regularization

Reducing radiation dose in dual energy computed tomography (DECT) is highly desirable but it may lead to excessive noise in the filtered backprojection (FBP) reconstructed DECT images, which can inevitably increase the diagnostic uncertainty. To obtain clinically acceptable DECT images from low-mAs acquisitions, in this work we develop a novel scheme based on measurement of DECT data. In this scheme, inspired by the success of edge-preserving non-local means (NLM) filtering in CT imaging and the intrinsic characteristics underlying DECT images, i.e. global correlation and non-local similarity, an averaged image induced NLM-based (aviNLM) regularization is incorporated into the penalized weighted least-squares (PWLS) framework. Specifically, the presented NLM-based regularization is designed by averaging the acquired DECT images, which takes the image similarity within the two energies into consideration. In addition, the weighted least-squares term takes into account DECT data-dependent variance. For simplicity, the presented scheme was termed as 'PWLS-aviNLM'. The performance of the presented PWLS-aviNLM algorithm was validated and evaluated on digital phantom, physical phantom and patient data. The extensive experiments validated that the presented PWLS-aviNLM algorithm outperforms the FBP, PWLS-TV and PWLS-NLM algorithms quantitatively. More importantly, it delivers the best qualitative results with the finest details and the fewest noise-induced artifacts, due to the aviNLM regularization learned from DECT images. This study demonstrated the feasibility and efficacy of the presented PWLS-aviNLM algorithm to improve the DECT reconstruction and resulting material decomposition.