Limited-angle Data Research Articles

Recovery of the spatially-variant deformations in dual-panel PET reconstructions using deep-learning

Dual panel PET systems, such as Breast-PET (B-PET) scanner, exhibit strong asymmetric and anisotropic spatially-variant deformations in the reconstructed images due to the limited-angle data and strong depth of interaction effects for the oblique LORs inherent in such systems. In our previous work, we studied time-of-flight (TOF) effects and image-based spatially-variant PSF resolution models within dual-panel PET reconstruction to reduce these deformations. The application of PSF based models led to better and more uniform quantification of small lesions across the field of view (FOV). However, the ability of such a model to correct for PSF deformation is limited to small objects. On the other hand, large object deformations caused by the limited-angle reconstruction cannot be corrected with the PSF modeling alone. In this work, we investigate the ability of deep-learning (DL) networks to recover such strong spatially-variant image deformations using first simulated PSF deformations in image space of a generic dual panel PET system and then using simulated and acquired phantom reconstructions from dual panel B-PET system developed in our lab at University of Pennsylvania. For the studies using real B-PET data, the network was trained on the simulated synthetic data sets providing ground truth for objects resembling experimentally acquired phantoms on which the network deformation corrections were then tested. The synthetic and acquired limited-angle B-PET data were reconstructed using DIRECT-RAMLA reconstructions, which were then used as the network inputs. Our results demonstrate that DL approaches can significantly eliminate deformations of limited angle systems and improve their quantitative performance.

Physics-informed Score-based Diffusion Model for Limited-angle Reconstruction of Cardiac Computed Tomography.

Cardiac computed tomography (CT) has emerged as a major imaging modality for the diagnosis and monitoring of cardiovascular diseases. High temporal resolution is essential to ensure diagnostic accuracy. Limited-angle data acquisition can reduce scan time and improve temporal resolution, but typically leads to severe image degradation and motivates for improved reconstruction techniques. In this paper, we propose a novel physics-informed score-based diffusion model (PSDM) for limited-angle reconstruction of cardiac CT. At the sampling time, we combine a data prior from a diffusion model and a model prior obtained via an iterative algorithm and Fourier fusion to further enhance the image quality. Specifically, our approach integrates the primal-dual hybrid gradient (PDHG) algorithm with score-based diffusion models, thereby enabling us to reconstruct high-quality cardiac CT images from limited-angle data. The numerical simulations and real data experiments confirm the effectiveness of our proposed approach.

Learning a microlocal prior for limited-angle tomography

Abstract Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. In this paper, a new method is introduced, based on machine learning and geometry, producing an estimate for interfaces between regions of different X-ray attenuation. The estimate can be presented on top of the reconstruction, indicating more reliably the separation between features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using convolutional neural networks, the visible part of the singular support is first extracted and then extended to the full domain, filling in the parts of the singular support that would otherwise be hidden due to the lack of measurement directions.

Sinogram Upsampling via Sub-Riemannian Diffusion with Adaptive Weighting

Computed tomography is a versatile imaging technique used to enable seeing internal structures of objects without opening or destroying them. This is possible through a process called tomographic reconstruction, which reconstructs images from projections of the object that are obtained by penetrating the object with beams of radiation, such as X-rays, from different angles. These projection data are often limited to low-resolution data in terms of projection angles. These limited or subsampled data make it difficult to obtain high-quality reconstruction results. Hence, upsampling projection data is necessary. In this paper, we propose a sinogram upsampling method via the sub-Riemannian diffusion process. We first lift the data into a feature space, and we fill in the missing angle parts by propagating information from the observed data to the missing parts. We observe that the sinogram with limited angle data has high directional dependency, and based on this observation, we suggest an adaptive weighting scheme to keep information propagating toward the missing regions. This adaptive weighting allows for diffusing toward the desired directions. The experimental results show the effectiveness of the proposed method in some scenarios regarding inpainting fine details, when compared to the existing model-based methods, such as Plug-and-Play and total generalized variation.

Efficient Algebraic Image Reconstruction Technique for Computed Tomography

Industrial computed tomography (CT) has seen widespread adoption within certain areas of non-destructive testing (NDT), with many commercial systems capable of acquisition and reconstruction of cone-beam CT data. The majority of these systems utilise reconstruction algorithms based on the traditional filtered back-projection (FBP) methods, which are imperfect with respect to limited-angle cone-beam data. These techniques are also inherently restricted in the source trajectories that can be utilised due to the use of Fourier slice theorem. This restricts FBP-based techniques to a circular or helical trajectory. Iterative reconstruction algorithms provide a solution to these limitations as the volume reconstruction does not depend on the location or orientation of the source and detector, allowing the possibility of scanning trajectories that satisfy well-known CT data-sufficiency conditions. This paper proposes a method of reconstruction based on computationally efficient computer graphics algorithms with data collected from points in 3D space not restricted to a single circular trajectory, which is useful within NDT for automated robotic inspection. The algorithms developed allow for rapid processing of the algebraic reconstruction technique (ART) for use with X-ray transmission data for CT reconstruction. Experimental results are presented for reconstructions for circular trajectory and points on a sphere to demonstrate the suitability for NDT applications.

A proof-of-concept study of an in-situ partial-ring time-of-flight PET scanner for proton beam verification.

Development of a PET system capable of in-situ imaging requires a design that can accommodate the proton treatment beam nozzle. Among the several PET instrumentation approaches developed thus far, the dual-panel PET scanner is often used as it is simpler to develop and integrate within the proton therapy gantry. Partial-angle coverage of these systems can however lead to limited-angle artefacts in the reconstructed PET image. We have previously demonstrated via simulations that time-of-flight (TOF) reconstruction reduces the artifacts accompanying limited-angle data, and permits proton range measurement with 1-2 mm accuracy and precision. In this work we show measured results from a small proof-of-concept dual-panel PET system that uses TOF information to reconstruct PET data acquired after proton irradiation. The PET scanner comprises of two detector modules, each comprised of an array of 4×4×30 mm3 lanthanum bromide scintillator. Measurements are performed with an oxygen-rich gel-water, an adipose tissue equivalent material, and in vitro tissue phantoms. For each phantom measurement, 2 Gy dose was deposited using 54 - 100 MeV proton beams. For each phantom, a Monte Carlo simulation generating the expected distribution of PET isotope from the corresponding proton irradiation was also performed. Proton range was calculated by drawing multiple depth-profiles over a central region encompassing the proton dose deposition. For each profile, proton range was calculated using two techniques (a) 50% pick-off from the distal edge of the profile, and (b) comparing the measured and Monte Carlo profile to minimize the absolute sum of differences over the entire profile. A 10 min PET acquisition acquired with minimal delay post proton-irradiation is compared with a 10 min PET scan acquired after a 20 min delay. Measurements show that PET acquisition with minimal delay is necessary to collect 15O signal, and maximize 11C signal collection with a short PET acquisition. In comparison with the 50% pick-off technique, the shift technique is more robust and offers better precision in measuring the proton range for the different phantoms. Range measurements from PET images acquired with minimal delay, and the shift technique demonstrate the ability to achieve <1.5 mm accuracy and precision in estimating proton range.

A sequential regularization based image reconstruction method for limited-angle spectral CT

In spectral computed tomography (CT), the object is respectively scanned under different x-ray spectra. Multiple projection data can be collectively used for reconstructing basis images and virtual monochromatic images, which have been used in material decomposition, beam-hardening correction, bone removal, and so on. In practice, projection data may be obtained in a limited scanning angular range. Images reconstructed from limited-angle data by conventional spectral CT reconstruction methods will be deteriorated by limited-angle related artifacts and basis image decomposition errors. Motivated by observations of limited-angle spectral CT, we propose a sequential regularization-based limited-angle spectral CT reconstruction model and its numerical solver. Both simulated and real data experiments validate that our method is capable of suppressing artifacts, preserving edges and reducing decomposition errors.

Effects of TOF Resolution Models on Edge Artifacts in PET Reconstruction from Limited-Angle Data.

Limited-angle data, such as data obtained from a dual-panel Breast-PET scanner, result in substantial image blur in directions coinciding with the missing cone of the image spectrum. On systems with time-of-flight (TOF) capabilities, this blur is reduced as given by the TOF uncertainty, with the image spectrum being correspondingly expanded into the missing spectral cone. Modeling of the TOF uncertainty in the reconstruction is expected to deconvolve this residual TOF blurring. We have however observed that, as a tradeoff, this TOF de-blurring process also introduces ringing artifacts at the edges, analogous to the edge effects observed with line-of-response (LOR) resolution modeling, which attempts to deconvolve the blur due to detector resolution effects. However, in the former case, the ringing artifacts are much wider due to the spatial extent of the TOF uncertainty as compared to the width of typical LOR resolution blur. We illustrate and investigate the effects of using matched, as well as under-modeled and over-modeled, TOF kernels on edge artifacts in reconstruction from limited-angle data, and compare them with TOF reconstructions of complete data. Although for the conventional data with full angular coverage the reconstruction is fairly insensitive to the exact size of the TOF kernel and TOF modeling does not produce ringing artifacts, it is not the case for the limited-angle data. We show that it is important to use some form of regularization of the TOF uncertainty deconvolution process within reconstruction of the limited-angle data, such as decreasing the TOF kernel size.

AirNet: Fused analytical and iterative reconstruction with deep neural network regularization for sparse-data CT.

Sparse-data computed tomography (CT) frequently occurs, such as breast tomosynthesis, C-arm CT, on-board four-dimensional cone-beam CT (4D CBCT), and industrial CT. However, sparse-data image reconstruction remains challenging due to highly undersampled data. This work develops a data-driven image reconstruction method for sparse-data CT using deep neural networks (DNN). The new method so-called AirNet is designed to incorporate the benefits from analytical reconstruction method (AR), iterative reconstruction method (IR), and DNN. It is built upon fused analytical and iterative reconstruction (AIR) that synergizes AR and IR via the optimization framework of modified proximal forward-backward splitting (PFBS). By unrolling PFBS into IR updates of CT data fidelity and DNN regularization with residual learning, AirNet utilizes AR such as FBP during the data fidelity, introduces dense connectivity into DNN regularization, and learns PFBS coefficients and DNN parameters that minimize the loss function during the training stage; and then AirNet with trained parameters can be used for end-to-end image reconstruction. A CT atlas of 100 prostate scans was used to validate the AirNet in comparison with state-of-art DNN-based postprocessing and image reconstruction methods. The validation loss in AirNet had the fastest decreasing rate, owing to inherited fast convergence from AIR. AirNet was robust to noise in projection data and content differences between the training set and the images to be reconstructed. The impact of image quality on radiotherapy treatment planning was evaluated for both photon and proton therapy, and AirNet achieved the best treatment plan quality, especially for proton therapy. For example, with limited-angle data, the maximal target dose for AirNet was 109.5% in comparison with the ground truth 109.1%, while it was significantly elevated to 115.1% and 128.1% for FBPConvNet and LEARN, respectively. A new image reconstruction AirNet is developed for sparse-data CT image reconstruction. AirNet achieved the best image reconstruction quality both visually and quantitatively among all methods under comparison for all sparse-data scenarios (sparse-view and limited-angle), and provided the best photon and proton treatment plan quality based on sparse-data CT.

Limited angle tomography for transmission X-ray microscopy using deep learning.

In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision with other system parts or high attenuation at certain tilting angles. Image reconstruction from such limited angle data suffers from artifacts because of missing data. In this work, deep learning is applied to limited angle reconstruction in TXMs for the first time. With the challenge to obtain sufficient real data for training, training a deep neural network from synthetic data is investigated. In particular, U-Net, the state-of-the-art neural network in biomedical imaging, is trained from synthetic ellipsoid data and multi-category data to reduce artifacts in filtered back-projection (FBP) reconstruction images. The proposed method is evaluated on synthetic data and real scanned chlorella data in 100° limited angle tomography. For synthetic test data, U-Net significantly reduces the root-mean-square error (RMSE) from 2.55 × 10-3 µm-1 in the FBP reconstruction to 1.21 × 10-3 µm-1 in the U-Net reconstruction and also improves the structural similarity (SSIM) index from 0.625 to 0.920. With penalized weighted least-square denoising of measured projections, the RMSE and SSIM are further improved to 1.16 × 10-3 µm-1 and 0.932, respectively. For real test data, the proposed method remarkably improves the 3D visualization of the subcellular structures in the chlorella cell, which indicates its important value for nanoscale imaging in biology, nanoscience and materials science.

Sparse and limited-angle CT image reconstruction using dictionary learning constrained by L1 norm

Reconstructed images from computed tomography (CT) using the algebraic reconstruction technique (ART) and simultaneous ART (SART) algorithms often suffer from obvious artefacts when only sparse and limited-angle projection data are available. Using the ability of dictionary learning (DL) in image feature extraction and sparse signal representation, a new iterative reconstruction algorithm, ART-DL-L1, is proposed to overcome the aforementioned limitations. This new algorithm is based on DL and an L1 norm constraint, combined with ART. An alternate iterative solving strategy based on an approach of 'ART first, then adaptive dictionary learning' is suggested and is explicitly described in a flowchart depicting the ART-DL-L1 algorithm. For both a noisy projection of 360° sparse data and limitedangle data of 120°, simulation reconstruction results from the classic Shepp-Logan image obtained using ART-DL-L1 appear to be better than those obtained using SART and total variation (TV) algorithms and also better than the cutting-edge ART-DL-L2 algorithm. Five evaluation metrics corresponding to the root-mean-square error (RMSE), the mean absolute error (MAE), the peak signal-to-noise ratio (PSNR), the residuals and the structural similarity (SSIM) index are adopted to estimate the reconstruction effect. The results suggest that the five metrics obtained using ART-DL-L1 outperform those obtained using the other three algorithms. The impact of using patches of various sizes played by the DL part in ART-DL-L1 is considered in the simulations and the patch size achieving the best reconstructed image quality is identified in this case as 25 (5 × 5). Overall, the proposed ART-DL-L1 algorithm may reduce artefacts and suppress noise from incomplete noisy projection CT imaging to some degree.

Far-Field Inversion for the Deep Interior Scanning CubeSat

This study aims at advancing mathematical and computational techniques for reconstructing the interior structure of a small solar system body via computed radar tomography (CRT). We introduce a far-field model for full-wave CRT and validate it numerically for an orbiting distance of 5 km using a synthetic three-dimensional target asteroid and sparse limited-angle data. As a potential future application of the proposed method, we consider the deep interior scanning CubeSat concept in which the goal is to localize macroporosities inside a rubble-pile near-earth asteroid with two small spacecraft carrying a bistatic radar.

An image reconstruction model regularized by edge-preserving diffusion and smoothing for limited-angle computed tomography

Limited-angle computed tomography is a very challenging problem in applications. Due to a high degree of ill-posedness, conventional reconstruction algorithms will introduce blurring along the directions perpendicular to the missing projection lines, as well as streak artifacts when applied on limited-angle data. Various models and algorithms have been proposed to improve the reconstruction quality by incorporating priors, among which the total variation, i.e. l1 norm of gradient, and l0 norm of the gradient are the most popular ones. These models and algorithms partially solve the blurring problem under certain situations. However, the fundamental difficulty remains. In this paper, we propose a reconstruction model for limited-angle computed tomography, which incorporates two regularization terms that play the role of edge-preserving diffusion and smoothing along the x-direction and y -direction respectively. Then, an alternating minimization algorithm is proposed to solve the model approximately. The proposed model is inspired by the theory of visible and invisible singularities of limited-angle data, developed by Quinto et al. By incorporating visible singularities as priors into an iterative procedure, the proposed algorithm could produce promising results and outperforms state-of-the-art algorithms for certain limited-angle computed tomography applications. Extensive experiments on both simulated data and real data are provided to validate our model and algorithm.

Compressed sensing-based reconstruction for computed tomography with translational trajectory

ABSTRACTThis study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.

An adaptive multiscale anisotropic diffusion regularized image reconstruction method for digital breast tomosynthesis.

As a special case of tomography, digital breast tomosynthesis (DBT) can realize quasi-3D image reconstruction for breast lesion detection from few-view and limited-angle projection data. For DBT image reconstruction, iterative algorithms are needed to suppress artifacts due to undersampling, and adaptive regularizations are necessary for preserving the edges of masses and calcifications. This paper presents a novel reconstruction method by regularizing projection onto convex sets (POCS) with multiscale Tikhonov-total variation (MTTV). The regularization, known as adaptive multiscale anisotropic diffusion, is able to preserve edges to a considerable extent and selectively suppress noise without introducing artifacts. The proposed method is referred to as MTTV-POCS and is evaluated quantitatively using 3D numerical breast and Shepp-Logan phantoms as well as two clinical volume images acquired from an advanced DBT machine. Experimental results show that the proposed method has better performance in metrics of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) over two existing methods: adaptive-steepest-descent-POCS (ASD-POCS) and selective-diffusion regularized simultaneous algebraic reconstruction technique (SD-SART). As indicated by the results, the proposed method is applicable to DBT for high-quality image reconstruction.

Traditional machine learning for limited angle tomography

The application of traditional machine learning techniques, in the form of regression models based on conventional, "hand-crafted" features, to artifact reduction in limited angle tomography is investigated. Mean-variation-median (MVM), Laplacian, Hessian, and shift-variant data loss (SVDL) features are extracted from the images reconstructed from limited angle data. The regression models linear regression (LR), multilayer perceptron (MLP), and reduced-error pruning tree (REPTree) are applied to predict artifact images. REPTree learns artifacts best and reaches the smallest root-mean-square error (RMSE) of 29HU for the Shepp-Logan phantom in a parallel-beam study. Further experiments demonstrate that the MVM and Hessian features complement each other, whereas the Laplacian feature is redundant in the presence of MVM. In fan-beam, the SVDL features are also beneficial. A preliminary experiment on clinical data in a fan-beam study demonstrates that REPTree can reduce some artifacts for clinical data. However, it is not sufficient as a lot of incorrect pixel intensities still remain in the estimated reconstruction images. REPTree has the best performance on learning artifacts in limited angle tomography compared with LR and MLP. The features of MVM, Hessian, and SVDL are beneficial for artifact prediction in limited angle tomography. Preliminary experiments on clinical data suggest that the investigation on more features is necessary for clinical applications of REPTree.

A Comparison of Preseason Body Composition and Phase Angle in NCAA Division I Female Athletes

Body composition has several implications for the overall health and performance of athletes. Phase angle, a marker of cellular integrity, nutritional status and distribution of intra- (ICW) and extracellular water (ECW) may indicate overtraining and poor nutrition. A phase angle less than 5° is used as a criterion of poor cellular integrity and nutritional status in non-athletic populations. However, limited phase angle, ICW and ECW data exists for collegiate athletes. PURPOSE: To evaluate the differences in measures of body composition between NCAA Division I female cross-country (XC), soccer (SOC) and basketball (BB) athletes. METHODS: Fifty female athletes (age: 19±1yrs; XC, n=19; SOC, n=19; BB, n=12) were assessed in the preseason. Body composition, including lean mass (LM), fat mass (FM), regional bone mineral density (BMD) of the lumbar spine (L1-L4), and hip (femur) were measured by DXA. Appendicular skeletal muscle adjusted by squared height (ASM index; kg/m2), LM index (LMI; kg/m2) and FM index (FMI; kg/m2) were calculated to compare relative body composition. Bioelectric impedance analysis was used to assess phase angle, ICW (%) and ECW (%). ANOVAs were used to analyze the data. Significance was accepted at p<0.05. RESULTS: XC had significantly lower ASMI (6.83±0.5 vs. 7.42±0.5 and 8.07±0.9kg/ m2, p<0.001), FMI (3.85±1 vs. 6.04±2 and 6.07±0.9kg/m2, p<0.001) and body fat % (18.5±5 vs. 25.5±5 and 27.4±9%, p=0.001) than SOC and BB. There were no differences in ASMI, FMI and body fat % between SOC and BB. LMI was significantly lower in XC (15.3±0.9kg/m2) compared to SOC (16.2±0.9kg/m2, p<0.001). XC had significantly greater ICW (58.8±2% vs. 54.3±2%, p<0.001) and lower ECW (41.2±2% vs. 45.7±2%, p<0.001) than BB. The average phase angle was 7.4±0.5° and did not differ between sports. BB had significantly greater lumber spine BMD (p<0.001), left femur BMD (p<0.001) and right femur BMD (p<0.001) than both XC and SOC. CONCLUSIONS: Our findings highlight the sport-specific differences in body composition measures that may inform strength and conditioning coaches and athletic trainers. Optimal body composition through quality nutrition and training programs improves performance, increases playing time, injury prevention and helps to assess overall health.

Image Reconstruction for Limited-Angle Electron Beam X-Ray Computed Tomography With Energy-Integrating Detectors for Multiphase Flows

We propose a new iterative X-ray computed tomography (CT) reconstruction algorithm for electron beam X-ray tomography of multiphase flows in metal pipes. This application uses limited-angle projections due to the fixed configuration, and semiconductor-type energy-integrating detectors. For the data-fitting objective function, the proposed method incorporates a nonlinear Gaussian model with object-dependent variance to approximate the compound Poisson distribution, and a dual material decomposition based on images of the volume fractions of metal (titanium) and liquid (water). The volume fraction-based material decomposition enables us to use a maximum sum constraint that helps address the ill-posed nature of the problem. Two different regularizers, $\ell _0$ norm and edge-preserving hyperbola regularizers, are applied differently on each volume fraction image based on the characteristics of objects in each image. A synthetic phantom simulation illustrates that the proposed algorithm enables the aforementioned CT system to achieve high quality images by minimizing artifacts induced by limited-angle data and beam hardening.

A separable quadratic surrogate total variation minimization algorithm for accelerating accurate CT reconstruction from few-views and limited-angle data.

Total variation minimization (TVM) is a popular and useful method for accurate CT reconstruction from few-views and limited-angle data. However, the optimization procedure of previous TVM-based algorithms is very time-consuming. The purpose of this paper was to accelerate the high image quality CT reconstruction from few-views and limited-angle data. A new optimization algorithm based on the optimization transfer principle is proposed. The proposed algorithm uses TVM as the regularization term of the cost function that ensures the quality of the CT image reconstructed from few-views and limited-angle data. Additionally, half of the square of the difference between the original projection and the forward projection is used as the fidelity term. We then proved that the regularization term, i.e., 2-norm TV, is a convex function. Based on the convexity of the regularization and fidelity terms, a separable quadratic surrogate (SQS) function was proposed to substitute the regularization and fidelity terms. The solution of the cost function can be obtained by minimizing the SQS function and building the next SQS function at the minimum point. Both numerical simulations and simulations using real experimental data showed that the proposed algorithm reconstruct high-quality CT image from few-views and limited-angle data. The differences between the image reconstructed by the proposed algorithm and the images reconstructed by the previous algorithms are very small. However, the proposed algorithm required less than 1/10 time of the computational time of the previous algorithms. The image quality is not assessed in a rigorous way. The proposed algorithm can greatly accelerate the accurate CT reconstruction from few-views and limited-angle data relative to previous algorithms.

Graph-cut based discrete-valued image reconstruction.

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.