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

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

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

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

SIGNIFICANCE

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

Spectral CT image reconstruction using a constrained optimization approach-An algorithm for AAPM 2022 spectral CT grand challenge and beyond

BACKGROUND

CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner-up team.

PURPOSE

This paper reports details of our PROSPECT algorithm (Prior-based Restricted-variable Optimization for SPEctral CT) and follow-up studies regarding the algorithm's accuracy and enhancement of its convergence speed.

METHODS

We formulated the reconstruction task as an optimization problem. PROSPECT employed a one-step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam-hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data.

RESULTS

Prior knowledge allowed a reduction of the number of unknown variables by85.9 % $85.9\%$ . PROSPECT algorithm achieved the average root of mean square error (RMSE) of3.3 × 10 - 6 $3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double-precision projection data reduced RMSE to1.2 × 10 - 11 $1.2\,\times \,10^{-11}$ . Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time.

CONCLUSIONS

PROSPECT algorithm achieved a high degree of accuracy and computational efficiency.

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.

Report on the AAPM deep-learning spectral CT Grand Challenge

BACKGROUND

This Special Report summarizes the 2022 AAPM Grand Challenge on Deep-Learning spectral Computed Tomography (DL-spectral CT) image reconstruction.

PURPOSE

The purpose of the challenge is to develop the most accurate image reconstruction algorithm possible for solving the inverse problem associated with a fast kilovolt switching dual-energy CT scan using a three tissue-map decomposition. Participants could choose to use a deep-learning (DL), iterative, or a hybrid approach.

METHODS

The challenge is based on a 2D breast CT simulation, where the simulated breast phantom consists of three tissue maps: adipose, fibroglandular, and calcification distributions. The phantom specification is stochastic so that multiple realizations can be generated for DL approaches. A dual-energy scan is simulated where the x-ray source potential of successive views alternates between 50 and 80 kilovolts (kV). A total of 512 views are generated, yielding 256 views for each source voltage. We generate 50 and 80 kV images by use of filtered back-projection (FBP) on negative logarithm processed transmission data. For participants who develop a DL approach, 1000 cases are available. Each case consists of the three 512 × 512 tissue maps, 50 and 80-kV transmission data sets and their corresponding FBP images. The goal of the DL network would then be to predict the material maps from either the transmission data, FBP images, or a combination of the two. For participants developing a physics-based approach, all of the required modeling parameters are made available: geometry, spectra, and tissue attenuation curves. The provided information also allows for hybrid approaches where physics is exploited as well as information about the scanned object derived from the 1000 training cases. Final testing is performed by computation of root-mean-square error (RMSE) for predictions on the tissue maps from 100 new cases.

RESULTS

Test phase submission were received from 18 research groups. Of the 18 submissions, 17 were results obtained with algorithms that involved DL. Only the second place finishing team developed a physics-based image reconstruction algorithm. Both the winning and second place teams had highly accurate results where the RMSE was nearly zero to single floating point precision. Results from the top 10 also achieved a high degree of accuracy; and as a result, this special report outlines the methodology developed by each of these groups.

CONCLUSIONS

The DL-spectral CT challenge successfully established a forum for developing image reconstruction algorithms that address an important inverse problem relevant for spectral CT.

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

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

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

BACKGROUND

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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

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

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

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

Accurate Image Reconstruction in Dual-Energy CT with Limited-Angular-Range Data Using a Two-Step Method

Dual-energy CT (DECT) with scans over limited-angular ranges (LARs) may allow reductions in scan time and radiation dose and avoidance of possible collision between the moving parts of a scanner and the imaged object. The beam-hardening (BH) and LAR effects are two sources of image artifacts in DECT with LAR data. In this work, we investigate a two-step method to correct for both BH and LAR artifacts in order to yield accurate image reconstruction in DECT with LAR data. From low- and high-kVp LAR data in DECT, we first use a data-domain decomposition (DDD) algorithm to obtain LAR basis data with the non-linear BH effect corrected for. We then develop and tailor a directional-total-variation (DTV) algorithm to reconstruct from the LAR basis data obtained basis images with the LAR effect compensated for. Finally, using the basis images reconstructed, we create virtual monochromatic images (VMIs), and estimate physical quantities such as iodine concentrations and effective atomic numbers within the object imaged. We conduct numerical studies using two digital phantoms of different complexity levels and types of structures. LAR data of low- and high-kVp are generated from the phantoms over both single-arc (SA) and two-orthogonal-arc (TOA) LARs ranging from 14∘ to 180∘. Visual inspection and quantitative assessment of VMIs obtained reveal that the two-step method proposed can yield VMIs in which both BH and LAR artifacts are reduced, and estimation accuracy of physical quantities is improved. In addition, concerning SA and TOA scans with the same total LAR, the latter is shown to yield more accurate images and physical quantity estimations than the former. We investigate a two-step method that combines the DDD and DTV algorithms to correct for both BH and LAR artifacts in image reconstruction, yielding accurate VMIs and estimations of physical quantities, from low- and high-kVp LAR data in DECT. The results and knowledge acquired in the work on accurate image reconstruction in LAR DECT may give rise to further understanding and insights into the practical design of LAR scan configurations and reconstruction procedures for DECT applications.

An Extended Primal-Dual Algorithm Framework for Nonconvex Problems: Application to Image Reconstruction in Spectral CT

Using the convexity of each component of the forward operator, we propose an extended primal-dual algorithm framework for solving a kind of nonconvex and probably nonsmooth optimization problems in spectral CT image reconstruction. Following the proposed algorithm framework, we present six different iterative schemes or algorithms, and then establish the relationship to some existing algorithms. Under appropriate conditions, we prove the convergence of these schemes for the general case. Moreover, when the proposed schemes are applied to solving a specific problem in spectral CT image reconstruction, namely, total variation regularized nonlinear least-squares problem with nonnegative constraint, we also prove the particular convergence for these schemes by using some special properties. The numerical experiments with densely and sparsely data demonstrate the convergence and accuracy of the proposed algorithm framework in terms of visual inspection of images of realistic anatomic complexity and quantitative analysis with metrics structural similarity, peak signal-to-noise ratio, mean square error and maximum pixel difference. We analyze the computational complexity of these schemes, and discuss the extended applications of this algorithm framework in other nonlinear imaging problems.

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.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Image reconstruction from data over two orthogonal arcs of limited-angular ranges

PURPOSE

Computed tomography (CT) scanning over limited-angular ranges (LARs) is of practical interest in possible reduction of imaging dose and time and in design of non-standard scans. This work aims to investigate image reconstruction for two non-overlapping arcs of LARs, and to demonstrate that they may allow more accurate image reconstruction than may a single arc of LAR.

METHODS

We consider a configuration with two non-overlapping arcs of LARs α₁ and α₂ , whose centers are separated by 90°, and refer to it as a two-orthogonal-arc configuration. Data are generated from a chest phantom with two-orthogonal-arc configurations over total angular coverage α_τ = α₁ + α₂ ranging from 18° to 180°, and images are reconstructed subsequently by use of the directional-total-variation (DTV) algorithm. For comparison, we also consider image reconstruction for a single-arc configuration of angular range α_τ . Quantitative metrics such as the normalized root-mean-square-error (nRMSE) are used for evaluation of image reconstruction accuracy.

RESULTS

Visual inspection and quantitative analysis of images reconstructed reveal that a two-orthogonal-arc configuration generally yields more accurate image reconstruction than does its single-arc counterpart. As total angular range α_τ increases, the DTV algorithm yields image reconstruction with enhanced accuracy, as expected. Also, if α_τ remains constant, the two-orthogonal-arc configuration with α₁ = α₂ generally leads to image reconstruction more accurate than those of two-orthogonal-arc configurations with α₁ ≠ α₂ , as the nRMSE of the former can be lower than that of the latter for up to more than one order of magnitude.

CONCLUSIONS

Appropriately designed two-orthogonal-arc configurations may be exploited for improving image-reconstruction accuracy in CT imaging with reduced angular coverage. This study may yield insights into the design of innovative CT scans for lowering scan time and radiation dose, and/or for avoiding scan collision in, e.g., C-arm CT.

Non-convex optimization based optimal bone correction for various beam-hardening artifacts in CT imaging

Tube of X-ray computed tomography (CT) system emitting a polychromatic spectrum of photons leads to beam hardening artifacts such as cupping and streaks, while the metal implants in the imaged object results in metal artifacts in the reconstructed images. The simultaneous emergence of various beam-hardening artifacts degrades the diagnostic accuracy of CT images in clinics. Thus, it should be deeply investigated for suppressing such artifacts. In this study, data consistency condition is exploited to construct an objective function. Non-convex optimization algorithm is employed to solve the optimal scaling factors. Finally, an optimal bone correction is acquired to simultaneously correct for cupping, streaks and metal artifacts. Experimental result acquired by a realistic computer simulation demonstrates that the proposed method can adaptively determine the optimal scaling factors, and then correct for various beam-hardening artifacts in the reconstructed CT images. Especially, as compared to the nonlinear least squares before variable substitution, the running time of the new CT image reconstruction algorithm decreases 82.36% and residual error reduces 55.95%. As compared to the nonlinear least squares after variable substitution, the running time of the new algorithm decreases 67.54% with the same residual error.

Dual-energy CT imaging with limited-angular-range data

In dual-energy computed tomography (DECT), low- and high-kVp data are collected often over a full-angular range (FAR) of 360^○. While there exists strong interest in DECT with low- and high-kVp data acquired over limited-angular ranges (LARs), there remains little investigation of image reconstruction in DECT with LAR data.Objective: We investigate image reconstruction with minimized LAR artifacts from low- and high-kVp data over LARs of ≤180^○by using a directional-total-variation (DTV) algorithm.Methods: Image reconstruction from LAR data is formulated as a convex optimization problem in which data-l₂is minimized with constraints on image's DTVs along orthogonal axes. We then achieve image reconstruction by applying the DTV algorithm to solve the optimization problem. We conduct numerical studies from data generated over arcs of LARs, ranging from 14^○to 180^○, and perform visual inspection and quantitative analysis of images reconstructed.Results: Monochromatic images of interest obtained with the DTV algorithm from LAR data show substantially reduced artifacts that are observed often in images obtained with existing algorithms. The improved image quality also leads to accurate estimation of physical quantities of interest, such as effective atomic number and iodine-contrast concentration.Conclusion: Our study reveals that from LAR data of low- and high-kVp, monochromatic images can be obtained that are visually, and physical quantities can be estimated that are quantitatively, comparable to those obtained in FAR DECT.Significance: As LAR DECT is of high practical application interest, the results acquired in the work may engender insights into the design of DECT with LAR scanning configurations of practical application significance.

Directional-TV algorithm for image reconstruction from limited-angular-range data

Investigation of image reconstruction from data collected over a limited-angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This reconstruction problem is well-known to be challenging, however, because it is highly ill-conditioned. In the work, we investigate optimization-based image reconstruction from data acquired over a limited-angular range that is considerably smaller than the angular range in short-scan CT. We first formulate the reconstruction problem as a convex optimization program with directional total-variation (TV) constraints applied to the image, and then develop an iterative algorithm, referred to as the directional-TV (DTV) algorithm for image reconstruction through solving the optimization program. We use the DTV algorithm to reconstruct images from data collected over a variety of limited-angular ranges for breast and bar phantoms of clinical- and industrial-application relevance. The study demonstrates that the DTV algorithm accurately recovers the phantoms from data generated over a significantly reduced angular range, and that it considerably diminishes artifacts observed otherwise in reconstructions of existing algorithms. We have also obtained empirical conditions on minimal-angular ranges sufficient for numerically accurate image reconstruction with the DTV algorithm.