Sparse-View CT Reconstruction

CT: Computed Tomography

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 31

Oct 7, 2026cs.CV

Gradient-Based Trajectory Optimisation over Continuous Poses for Sparse-View Cone-Beam CT

Trajectory optimisation for cone-beam computed tomography (CT) determines which information sparse-view scans acquire. Fixed candidate pools prevent off-grid refinement and require new object-specific precomputation for each acquisition manifold. We make every source pose an individual continuous variable and move all poses jointly by gradient ascent on the scanner's kinematic manifold. The objective combines soft-Tuy plane coverage, continuous View Covariance Loss, and an analytic attenuation-aware ray-bundle penalty. The same optimiser handles circular, limited C-arm, two-axis, and freesphere parametrisations. On a Defrise flange, continuous selection recovers laminar defects invisible to a circular orbit, matches discrete swap search on the free sphere at the sparser budget, and leads at the denser one, with the same objective evaluated in every arm. A moderate elevation band already recovers most of the free-sphere gain at the defects, so the same optimiser transfers to bounded scanner envelopes. Photon noise preserves the ordering on the flange and compresses it on a dense fuel nozzle. Sparseprescan planning benefits from matching prescan and planned acquisition manifolds. Selection takes seconds rather than minutes without an object-specific reconstruction basis. Prescan-planned poses were executed on a robot CT bench and reconstructed in a common frame, demonstrating feasibility but no consistent metric gain over uniform band sampling. Continuous pose optimisation incorporates attenuation and scanner constraints directly into sparse-view acquisition design.

Linda-Sophie Schneider, Simon Wittl, Gabriel Herl +1

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Deggendorf Institute of Technology, Germany

Trajectory Optimization Cone-Beam CT Computed Tomography Sparse-View CT Reconstruction

Oct 7, 2026cs.CV

PhyDiCT: Plug-and-Play CT Reconstruction from Sparse X-Rays via Differentiable Rendering and Strong Priors

Reconstructing 3D Computed Tomography (CT) images from a few X-ray projections is a highly ill-posed inverse problem due to the loss of volumetric information. We propose PhyDiCT, a training-free framework that integrates a differentiable Physics-based forward model, grounded in the Beer-Lambert law, with a text-conditioned Diffusion as a strong prior to reconstruct 3D lung CT images. We refer to our approach as training-free since the prior model is used without fine-tuning, and our goal is to steer the denoising procedure to generate samples consistent with X-ray observations. We guide the diffusion generation using Split Gibbs sampling to jointly optimize for projection fidelity (reward) and consistency with prior knowledge. Also, we introduce a test-time refinement step that enhances image realism and anatomical coherence. We extensively evaluate our method on publicly available 3D CT datasets using both perceptual and semantic metrics, demonstrating that it surpasses existing plug-and-play diffusion and fully trained reconstruction approaches. Our findings highlight that combining a strong generative prior with the underlying physics of image formation substantially improves reconstruction quality, e.g., 7.5% improvement on SSIM compared to full training methods. Code will be released at https://github.com/batmanlab/PhyDiCT.

Weicheng Dai, Shantanu Ghosh, Kayhan Batmanghelich

Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA

Sparse-View CT Reconstruction 3D Medical Imaging Diffusion-Based Inverse Problems Physics-Informed Diffusion Models

Sep 29, 2026cs.CV

TomoTransformer: Towards a Foundation Model for CT Reconstruction

Supervised deep learning has advanced sparse-view tomographic reconstruction. However, conventional models, which typically map filtered back-projection (FBP) images or sinograms to clean reconstructions, are brittle under distribution shifts. Because they require retraining whenever projection counts and angles, detector resolutions, or data distributions change, their deployment in real-world applications remains limited. To address this, we introduce TomoTransformer, a transformer-based architecture that treats each \textit{local} filtered projection as an individual token and predicts missing views via self-attention. Crucially, TomoTransformer operates in a \emph{back-projection space} that separates projections across spatial locations, making view interpolation geometrically well-posed and invariant to detector size. This design yields a single foundation model that can process any number of input projections, at arbitrary angular locations and detector dimensions, and query any number of target angles without retraining. Trained on a large-scale dataset spanning diverse medical CT anatomies and natural images, TomoTransformer generalizes effectively across anatomies, materials, and resolutions. Extensive evaluations on several benchmark sparse-view datasets show that TomoTransformer significantly outperforms concurrent multi-purpose models like ViewTrans and matches or exceeds strong protocol-specific baselines, while remaining fully agnostic to the number of input and target projections. Furthermore, the model demonstrates robust zero-shot generalization on real experimental nanoscale brain data collected from an X-ray synchrotron, showcasing its practical utility for real-world applications.

AmirEhsan Khorashadizadeh, Benjamín Béjar

Swiss Data Science Center (SDSC) in Paul Scherrer Institute (PSI), Villigen, Switzerland.

Medical Imaging Foundation Models Image Reconstruction Sparse-View CT Reconstruction

Sep 9, 2026cs.CV

Shape-guided Gaussian Splatting for Sparse-View X-ray 3D Reconstruction

Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: https://github.com/polyshape-lab/ShapeGuidedGaussian

Pranav Poudel, Florence Dell'Aniello Picard, Nairouz Shehata +2

Polytechnique Montréal, Canada · Mila - Quebec AI Institute, Canada · CHUM - University of Montreal Hospital, Canada

3D Gaussian Splatting 3D Medical Imaging Statistical Shape Modeling Sparse-View CT Reconstruction

Aug 5, 2026cs.CV

Revisiting Pose Sensitivity in Splat-based Computed Tomography under Sparse-view Reconstruction

X-ray computed tomography (CT) reconstructs volumetric representations of objects from projection images obtained by transmitting X-rays through a target. Recent splat-based tomography, which represents a volume as a continuous distribution of 3D Gaussians, has demonstrated both high reconstruction quality and fast convergence in cone-beam sparse-view CT. However, when deployed in real CT systems with limited and non-uniform view distributions, we observe distinctive streak and strip artifacts that are far more pronounced than in conventional reconstruction methods. Through detailed analysis, we show that these artifacts primarily originate from pose inaccuracies in the acquisition geometry rather than from view sparsity itself. We revisit pose sensitivity in the splatting formulation and derive a stable gradient-based framework that jointly refines geometric parameters during reconstruction. Our study not only identifies how pose perturbations propagate through the differentiable projection operator but also reveals why splat-based CT is particularly vulnerable to geometric misalignment. The resulting formulation remains lightweight and easily integrable into existing pipelines while substantially improving reconstruction fidelity under real-world sparse-view conditions.

Kiseok Choi, Hyeongjun Cho, Inchul Kim +1

KAIST

3D Gaussian Splatting Cone-Beam CT Sparse-View CT Reconstruction Computed Tomography

Jul 24, 2026physics.med-ph

Agentic Autoresearch for CT Reconstruction

Comparing CT reconstruction methods fairly is labor-intensive and largely manual, and many benchmarks use idealized data. We ask whether a large language model (LLM) agent can do the labor of reconstruction research on its own, and whether a ranking measured on ideal data predicts behavior under realistic noise. We built an agentic loop: the agent edits a solver, runs a short cluster job, reads one frozen metric, and revises. The metric is a calibrated headroom score against the FBP baseline, inside the field of view; every method shares the same differentiable fan-beam projector. We benchmarked 26 methods on Mayo low-dose CT (noise-limited) and a 128-view sparse-view breast task from the noiseless DL-Sparse-View Challenge, with validation-selected iterations scored on a held-out test set. Every trained breast model was then re-scored on noisy inputs (I_0 = 10^5 photons) without retraining, and separately retrained on matched noise. The agent independently implemented, tuned, and benchmarked all 26 methods, and recombined them into a compact solver of 969 parameters that ties the top Mayo tier at the 1% level using 0.4% of the champion's parameters. Benchmarking gives a tier of statistically indistinguishable top methods, not one winner. Mild input noise nearly inverts the breast ranking: the noiseless champion (a supervised image denoiser, hr 0.89) collapses to 0.00, while a learned primal-dual method rises to champion (0.72 to 0.93). An ideal-data leaderboard therefore does not predict robustness. The inversion is a transfer effect, not a permanent deficit: retraining on matched noise restores much of the clean ranking (Spearman rho 0.04 to 0.61). Noise is only the easiest confounder in an open-ended set (beam hardening, scatter, anatomy, disease), so no single-factor challenge certifies generality. Benchmarks should model a broad spectrum of realistic factors at once.

Andreas Maier, Lucas Kachelriess, Siming Bayer +4

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany · Department Artificial Intelligence in Biomedical Engineering (AIBE), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany · Universitätsklinikum Erlangen (UKER), Erlangen, Germany +2

AI for Science Sparse-View CT Reconstruction Noise Robustness Computed Tomography

Jul 15, 2026cs.CV

$K$ -NeAS: Scalable Multi-Material CT Reconstruction Using Neural SDFs

Computed Tomography (CT) carries significant ionizing radiation risks, driving the need for sparse-view reconstruction. Implicit scene representations (ISRs) address this by recovering continuous volumetric attenuation fields directly from sparse projections, and recent geometry-aware extensions jointly model surface geometry alongside attenuation to improve fidelity and enable clean tissue segmentation without manual thresholding. However, these methods remain limited by manually tuned attenuation bounds and rigid two-material constraints. This paper proposes

K

-NeAS, a unified and scalable architecture for automated, multi-material surface reconstruction. We replace independent material networks with a shared latent backbone and introduce a fully differentiable

K

-material sequential soft selector to model an arbitrary number of overlapping tissues. To eliminate manual tuning, we automate attenuation bounding using a Gaussian Mixture Model (GMM) and implement a scheduled auxiliary floater loss to mitigate geometric hallucinations common under extreme sparsity. Evaluated across four clinical Cone-Beam CT (CBCT) datasets,

K

-NeAS successfully scales to arbitrary material counts, achieving superior 3D volumetric fidelity at

K=3

materials on complex multi-tissue regions such as the Abdomen (

33.28\text{ dB}

3D PSNR vs.

31.40\text{ dB}

single-material NeAS baseline, a

+1.88\text{ dB}

improvement). Furthermore, our model exhibits enhanced robustness under sparse-sampling conditions, outperforming baseline 3D PSNR by up to

1.17\text{ dB}

under 5- and 10-view constraints.

Daksh K. Shah, Emmanouil Nikolakakis, Razvan Marinescu

University of California, Santa Cruz

Cone-Beam CT Implicit Neural Representations Sparse-View CT Reconstruction Computed Tomography

Jul 15, 2026cs.CV

Posterior Variance Is a Constraint Map, Not an Error Map: Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT

Radiative Gaussian splatting reconstructs sparse-view CT fast and accurately, and recent work attaches per-Gaussian posteriors to yield per-voxel uncertainty maps. We ask what such a map actually measures: posterior variance is a data-constraint map, not an error map -- its alarms are trustworthy, its all-clears are not. Exploiting the strict linearity of X-ray rendering in the per-Gaussian densities, we derive a clamp-aware closed form that the unchanged rasterizer evaluates exactly in one forward pass, in volume and projection space: the infinite-sample limit of the sampling estimator of concurrent work, at ~8x lower cost. On the official 15-scene benchmark this uncertainty ranks true error on 14 of 15 scenes. Restricted to the object interior -- the tissue a clinician reads -- the ranking collapses (median Spearman 0.11, 0/15 pass), identically for a deep ensemble and for a strictly positive log-normal posterior: three constructions, two estimator families, no survivors. The mechanism is structural: about 90% of in-object error is bias that reproduces across retrainings, invisible to model disagreement; 73-81% of the full-volume correlation is carried by object/surround contrast; and an exactly solvable control puts the observed in-object ranking 4-5x below what a perfectly calibrated posterior with the same sigma-spread would score. The error scale, by contrast, is an engineering problem, and we solve it: reparameterizing the posterior contracts the cross-scene temperature spread from 19.3x to 2.6x, one scene-agnostic temperature transfers to unseen scenes (10/15 leave-one-scene-out), and the repaired scale tracks photon count at the Poisson-predicted -1/2 power. We distill evaluation practice that would have caught the illusion -- masked calibration, seed-wise bias decomposition, an exact-posterior reference -- and release all protocols, seeds and per-run evidence.

Chulin Zhao, Yiran Xu, Shu Liu

1Dundee International Institute, Central South University · 2Central South University

3D Gaussian Splatting Uncertainty Quantification Sparse-View CT Reconstruction Uncertainty Calibration

Jul 14, 2026eess.IV

Exact and Calibrated Diffusion Reconstruction for Digital Breast Tomosynthesis

Limited-angle digital breast tomosynthesis (DBT) reconstructs a volume from a few low-dose projections over a narrow arc. At a representative nine-view,

25^{\circ}

protocol more than 98% of image space is unmeasured, so a learned prior must supply structure in the missing wedge. Conditional diffusion priors achieve strong perceptual quality here but leave three clinical obstacles: inexact data consistency, unlocalized hallucination, and uncalibrated uncertainty. We enforce measurements exactly by replacing the per-step proximal update of a conditional diffusion sampler with exact Euclidean projection onto the data-consistent set, computed via an

m

-dimensional dual system with a one-time Gram matrix

AA^{\top}

factorization. This projection costs 4.5 ms per step (a

248\times

speedup) and drives the data residual to the double-precision floor (

2.4\times10^{-13}

). We prove it is the

ρ\to0

limit of the proximal step, provide a no-harm theorem, and show that exactly consistent sample ensembles have variance supported on null(

A

). Thus, the mean's entire error lies in the unmeasured subspace covered by the uncertainty map. On patient-derived breast phantoms, this improves fidelity at no depth-resolution cost. Conversely, a proximal step applied post-update degrades quality, isolating the consistency step's placement as decisive. Isotonic recalibration brings the ensemble spread to a calibrated error scale (expected calibration error

0.029\to0.008

; standardized error

4.7\to0.96

), ranking errors better than the pure prior. We also repair a 20.3% adjoint mismatch in a deployed projector via a materialized operator of record. This is the first data-consistent, uncertainty-calibrated learned reconstruction for limited-angle DBT. The solver naturally relaxes to discrepancy-ball and maximum-a-posteriori modes for noisy measurements.

Imade Bouftini

Image Reconstruction Sparse-View CT Reconstruction Computed Tomography Diffusion Posterior Sampling Uncertainty Calibration

Jul 12, 2026cs.CV

Design Choices in Splitting-Based Self-Supervised Sparse-View CT Reconstruction

Self-supervised data splitting has emerged as a promising paradigm for sparse-view CT reconstruction, enabling training from incomplete measurements without fully sampled ground truth. However, the influence of key design choices, including partitioning strategy, preprocessing, and inference, remains insufficiently understood. In this work, we introduce a unified framework that decomposes splitting-based reconstruction into these three components, enabling controlled comparison of existing methods and two incremental extensions: multi-partition splitting and an alternative inference strategy. Experiments on simulated LoDoPaB-CT data under independent and correlated noise, together with validation on the real-world 2DeteCT dataset, show that the optimal partitioning strategy strongly depends on the measurement noise structure. Lattice-based splitting performs favorably under independent noise, whereas angular masking is more robust under correlated noise and real measured data. Multi-partition splitting consistently improves over pure projection-wise splitting in several settings. Complementary perceptual and structural metrics, including LPIPS and HaarPSI, reveal differences between masking strategies that are less apparent from PSNR and SSIM alone. These results provide practical guidelines for designing self-supervised sparse-view CT reconstruction methods and highlight the limitations of common independence assumptions in realistic imaging environments.

Nadja Gruber, Lukas Neumann, Ander Biguri +3

Department of Computer Science, University of Innsbruck, Austria. · Institute of Basic Sciences in Engineering Science, University of Innsbruck, Austria. · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. +3

Self-Supervised Learning Sparse-View CT Reconstruction Computed Tomography

Jul 12, 2026cs.CV

Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation

Objective. Existing quadratic unconstrained binary optimization (QUBO)-based sparse-view computed tomography (CT) reconstruction neglects photon-counting statistics and anatomical heterogeneity. We address both limitations within the QUBO framework.Approach. We propose a quantum compressed-sensing CT method combining penalized weighted least squares (PWLS) and guided total variation (GTV). PWLS weights projection residuals by photon-count reliability, whereas GTV uses gradients from a prior image reconstructed by the simultaneous algebraic reconstruction technique (SART) to preserve edges and suppress noise in homogeneous regions. After binary encoding, both terms form a unified QUBO model. Experiments used four 40 times 40 CT images under a 10-view fan-beam geometry with Poisson noise. Comparisons included conventional reconstruction methods, QUBO variants, gradient descent, simulated annealing, and a D-Wave hybrid quantum-classical solver.Main results. PWLS-GTV achieved the best reconstruction quality across all cases. In the representative chest case, it reached a peak signal-to-noise ratio (PSNR) of 36.64 dB, compared with 22.48 dB for SART, the best conventional baseline. GTV consistently outperformed conventional total variation. Simulated annealing and the D-Wave hybrid solver produced similar reconstructions, whereas gradient descent was ineffective. Repeated hybrid-solver runs showed stable performance.Significance. The framework incorporates photon-statistical weighting and structure-guided regularization into QUBO-based CT reconstruction without changing its quadratic form, providing a proof of concept for quantum-assisted sparse-view CT reconstruction.

Yuwen Zhang, Yujie Liu, Ao Wang +4

Department of Medical Imaging Technology, Peking University Health Science Center, Beijing, China

Sparse-View CT Reconstruction Quadratic Unconstrained Binary Optimization Compressed Sensing

Jul 10, 2026eess.IV

Robustness and Stability Analysis of Differentiable Shift-Variant FBP for Cone-Beam CT under Challenging Acquisition Settings

The differentiable shift-variant filtered backprojection (SV-FBP) framework enables data-driven estimation of redundancy weights for cone-beam CT reconstruction under general source trajectories, removing the need for analytically derived weighting schemes. In this work, we present a systematic study of the robustness and adaptability of differentiable SV-FBP under challenging acquisition settings. We show that the framework remains stable across highly irregular and discontinuous trajectories, indicating that reconstruction performance is largely insensitive to trajectory ordering or continuity. Instead, the spatial distribution of sampling points plays a more dominant role. Under sparse-view conditions, differentiable SV-FBP achieves competitive reconstruction quality while providing an order-of-magnitude reduction in computation time compared to iterative reconstruction methods at moderate sampling densities. However, we identify a clear transition regime under severe undersampling, where the absence of iterative data consistency leads to performance degradation. Furthermore, we demonstrate that the framework remains applicable to non-planar multi-isocenter geometries, such as Lissajous-saddle trajectories, without requiring architectural modifications. These findings provide new insights into the behavior and limitations of the differentiable SV-FBP model and highlight it as a flexible and efficient solution for non-standard and robotic CBCT acquisition scenarios.

Chengze Ye, Linda-Sophie Schneider, Yipeng Sun +5

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

Cone-Beam CT Image Reconstruction Sparse-View CT Reconstruction Computed Tomography

Jul 4, 2026cs.LG

SAVER: Stochastic Adaptive Variance-Driven Exploration and Reconstruction for Low-Dose Computed Tomography

Computed Tomography (CT) is indispensable in clinical diagnostics, yet minimizing radiation dose without compromising image quality remains a critical challenge. Conventional low-dose protocols often rely on fixed, uniform angular sampling, independent of the underlying structural complexity of organs of individual patients. We propose ``Stochastic Adaptive Variance-Driven Exploration and Reconstruction'' (SAVER), an adaptive data acquisition framework that selects projection angles in real-time based on the statistical variance of acquired data. Utilizing a Softmax-based stochastic scheduling scheme with simulated annealing, SAVER prioritizes directions with high structural information while maintaining necessary exploration. Numerical experiments across 8 diverse phantoms demonstrate that SAVER achieves consistently higher reconstruction fidelity than conventional random sampling, particularly for objects with high structural anisotropy. Furthermore, the proposed method exhibits robust performance under significant measurement noise. By dynamically reallocating radiation dose to the most informative projections, SAVER provides a mathematically-grounded approach to maximize diagnostic quality per unit of radiation dose, marking a shift toward sample-dependent, data-driven CT acquisition.

Shunta Nonaga, Koji Tabata, Junya Honda +3

Graduate School of Chemical Sciences and Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan. · Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0020, Japan · Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan. +7

Sparse-View CT Reconstruction Adaptive Sampling Computed Tomography

Jun 29, 2026cs.CV

A Dual-domain Refinement Network with FBP-based Jacobian Learning for Sparse-view Dual-Energy CT Material Decomposition

Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely used in medical imaging. While sparse-view acquisition can lower radiation exposure, it makes DECT material decomposition even more challenging, as the problem is nonlinear and ill-posed. Existing deep unrolling approaches generally do not explicitly incorporate the Jacobian operator induced by the nonlinear forward model, and their sparsity priors are still mainly built on conventional convolutions, which are insufficient for modeling global structural information. This study addresses the challenge of DECT multi-material decomposition in sparse-view settings by representing it as a sparse-regularized nonlinear least-squares problem. To solve it, we propose an iterative dual-domain refinement network (DECT-DRNet). In each iteration, the filtered back-projection (FBP)-based Jacobian approximation module is used first to generate an intermediate material decomposition result. Here, we characterize the forward process of material decomposition using a nonlinear operator, and then construct a theoretically grounded learnable approximation of the adjoint Jacobian operator by integrating the FBP algorithm with a U-Net into the backward process. In addition, to address the limitation of existing deep learning-based decomposition methods in globally suppressing noise and artifacts, we introduce a learnable sparse dual domain regularization term that incorporates Fourier convolutional residual blocks. This refinement block combines geometric feature extraction in the image domain with noise suppression in the frequency domain, allowing the model to capture both global and local features while maintaining structural details. DECT-DRNet demonstrates its ability to achieve more accurate material decomposition under sparse-view conditions.

Qian Liu, Xiaohong Fan, Ke Chen +3

School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education, Xiangtan 411105, China · College of Mathematical Medicine, Zhejiang Normal University, Jinhua 321004, China · Department of Mathematics and Statistics, University of Strathclyde, G1 1XH Glasgow, U.K. +1

Sparse-View CT Reconstruction Operator Learning Computed Tomography

Jun 25, 2026eess.IV

Enabling self-supervised learned primal dual with Noise2Inverse

X-ray computed tomography reconstruction is an ill-posed inverse problem, particularly in low-dose and sparse-angle settings where measurements are noisy and incomplete. While learned reconstruction methods such as the Learned Primal-Dual algorithm achieve strong performance, they typically rely on supervised training with access to ground-truth data, which is often unavailable in practice. In this work, we propose a self-supervised reconstruction method by extending the Noise2Inverse framework to the Learned Primal-Dual algorithm. The resulting approach, called Noise2Inverse Learned Primal-Dual (N2I-LPD), enables training of a learned iterative reconstruction operator without ground-truth images by exploiting the statistical independence of noise in distinct measurements with respect to angular rotation of the CT-scan. We compare the proposed method with classical reconstruction methods, as well as neural network-based approaches such as a U-Net trained within the same N2I framework. The results demonstrate that N2I-LPD achieves improved reconstruction quality, highlighting the potential of combining learned reconstruction operators with self-supervised training strategies for practical CT imaging scenarios where ground-truth data is unavailable.

Antti Sällinen, Siiri Rautio, Santeri Kaupinmäki +1

Research Unit of Mathematical Sciences, University of Oulu, Finland · Department of Mathematics and Information Science, Josai University, Japan · Department of Computer Science, University College London, United Kingdom

Self-Supervised Learning Image Reconstruction Sparse-View CT Reconstruction Computed Tomography Inverse Problems

Jun 23, 2026cs.CV

Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstruction

Sparse-view computed tomography (SVCT) reduces radiation exposure and acquisition time, but the limited number of projection views makes the reconstruction problem severely ill-posed and leads to streak artifacts when analytical methods are used. Plug-and-Play (PnP) methods provide an effective way to combine data fidelity with learned image priors, while stochastic PnP methods further improve robustness by matching the denoiser input distribution through re-noising. However, these methods often require many iterations to converge, which limits their practical efficiency. In this work, we propose a multilevel (ML) stochastic PnP method for SVCT that accelerates stochastic PnP reconstruction. We highlight that, in the stochastic setting, directly enforcing prior coherence across levels would require accurately estimating fine-level prior gradients through multiple denoiser function evaluations, which substantially increases the computational cost. Motivated by this observation, we perform the multilevel steps in multiresolution analysis (MRA) approximation spaces. This choice is supported by the structure of the wavelet decomposition, which causes the prior-coherence correction to vanish in expectation, thereby avoiding costly estimation of fine-level stochastic prior gradients for the coarse-level corrections. Experiments on SVCT reconstruction show that our method, called Multilevel Stochastic Plug-and-Play (ML-SPnP), achieves reconstruction quality comparable to state-of-the-art methods while substantially reducing runtime.

Antoine De Paepe, Alexandre Bousse, Dimitris Visvikis

LaTIM, Inserm, UMR 1101, Université de Bretagne Occidentale, Brest, France

Image Reconstruction Sparse-View CT Reconstruction Inverse Problems

Jun 23, 2026cs.CV

Quantum CT via Dynamic Interval Encoding and Prior-Balanced QUBO Reconstruction

Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantum--classical solvers. For grayscale CT, however, image encoding is constrained by the binary-variable budget: fixed global bit-plane encodings increase QUBO size and coupling complexity as gray-level precision improves, whereas low-bit encodings introduce quantization error. We propose a QUBO-based grayscale CT reconstruction framework that combines dynamic interval encoding with prior-balanced optimization. Each refinement round encodes active pixels only within local gray-level intervals around the current estimate, and a boundary-hit-guided update rule adaptively switches between search expansion and local refinement. To improve optimization stability, the method balances projection-domain data consistency and an edge-preserving quadratic prior before forming the final QUBO. Sparse-view and limited-angle fan-beam CT experiments show that the proposed method recovers structures and gray-level distributions more faithfully than the evaluated analytic, iterative, variational, and representation-based baselines. Expressivity analysis and ablation studies further indicate that the improvement mainly arises from effective gray-level representation through dynamic local encoding and more stable data-fidelity--prior coupling. Experiments on the D-Wave hybrid binary quadratic model (BQM) solver further demonstrate that the formulation is executable on a hardware-backed hybrid quantum--classical backend.

Ao Wang, Yikuang Yuluo, Yujie Liu +7

Image Reconstruction Sparse-View CT Reconstruction Quadratic Unconstrained Binary Optimization Computed Tomography

Jun 21, 2026cs.CV

Projection-Volume Fidelity Divergence: Diagnosing and Controlling Optimization Drift in Sparse-View 3D Gaussian Tomography

Sparse-view computed tomography is a severely ill-posed inverse problem, where recent 3D Gaussian Splatting methods offer an efficient explicit representation for tomographic reconstruction. However, we find that projection-domain optimization can be misleading in this setting: the rendered projections may continue to improve while the reconstructed volume deteriorates. We identify this failure mode as Projection-Volume Fidelity Divergence (PVFD), a representation-level optimization drift caused by anisotropic Gaussian deformation and view-specific primitive co-adaptation under sparse Radon constraints. To characterize this behavior, we introduce geometry- and volume-level diagnostics that measure needle-like Gaussian degeneration and the stability of the voxelized density field. Based on these observations, we propose LADES, a ground-truth-free optimization controller for sparse-view Gaussian tomography. LADES combines Linearly Annealed Dropout, which applies strong stochastic masking in early training to disrupt premature primitive co-adaptation and gradually restores full capacity for structural consolidation, with Structure-Aware Early Stopping, which terminates densification according to the saturation of Gaussian population growth rather than validation PSNR. Experiments on sparse-view CT reconstruction show that LADES improves volumetric fidelity, suppresses structural degeneration, and substantially reduces training time while maintaining competitive projection accuracy. These results suggest that robust Gaussian-based tomography requires monitoring and controlling volumetric structure, rather than optimizing projection fit alone.

Yikuang Yuluo, Ao Wang, Shen Kuan +6

1Chongqing University, Chongqing, China · 2Peking University Health Science Center, Beijing, China

3D Gaussian Splatting Adaptive Gaussian Densification Sparse-View CT Reconstruction

Jun 15, 2026cs.CV

LUCID: Learned Undersampling-Adaptive Consistency-Guided Inference with Deterministic Flow Matching for Sparse-View CT Reconstruction

Sparse-view CT reduces radiation dose and scanning time by acquiring fewer projection views, but angular undersampling makes reconstruction severely ill-posed, causing streak artifacts, structural blurring, and loss of fine details. Existing supervised methods are often tied to specific sampling settings, whereas generative methods may introduce anatomically inconsistent hallucination-like structures under severe undersampling. We propose Lucid, a sparsity-adaptive, consistency-guided reconstruction framework based on a Flow Matching generative prior for sparse-view CT. Lucid is trained only on high-quality CT images to learn a continuous transport between a Gaussian distribution and the high-quality CT image distribution, independent of view sampling. During inference, the sampling sparsity level is explicitly incorporated to adapt the generative trajectory of a single pretrained model. Specifically, Lucid constructs a degradation-matched initial state by sparsity-weighted fusion of the sparse-view FBP image and Gaussian noise, performs sparsity-modulated Flow Matching updates, and applies projection-domain data-consistency correction after each prior update. Experiments under multiple sparse-view settings show that Lucid achieves stable reconstruction performance across different sampling densities, improves image quality and structural fidelity, and reduces the risk of hallucination-like structures in generative sparse-view CT reconstruction.

Jigang Duan, Jiayi Wang, Heran Wang +3

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · National Center for Applied Mathematics Beijing, Capital Normal University and Academy for multidisciplinary studies, Capital Normal University, Beijing, 100048, China

Sparse-View CT Reconstruction Computational Imaging Computed Tomography Image Inverse Problems

May 26, 2026eess.IV

Unsupervised Deep Image Prior for Sparse-View and Limited-Angle Electron Tomography

Electron tomography (ET) plays an important role in the three-dimensional (3D) characterization of nanomaterials. However, under limited-angle and sparse-view conditions, conventional algorithms produce degraded reconstructions, which compromise the quality and interpretability of resulting 3D data. In this paper, we present deep image prior (DIP), an unsupervised deep learning (DL) approach, for highly degraded tomography acquisitions and demonstrate, using simulated data, that its performance is comparable to that of supervised approaches requiring training datasets, even for tilt ranges as limited as 60° and tilt increments of 10°. We then apply it to experimental data and show that it enables reliable 3D quantification under both sparse-view and limited-angle conditions, highlighting its potential for a wide range of materials and acquisition modalities.

Serge Brosset, Daniel del Pozo Bueno, Thomas David +3

a Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France. · b Univ. Grenoble Alpes, CEA, Liten, F-38000 Grenoble, France. · c CEA, Joliot, NeuroSpin, Gif-sur-Yvette Cedex 91191, France. +1

Sparse-View CT Reconstruction Computed Tomography Image Inverse Problems

May 5, 2026cs.CV

GeoTopoDiff: Learning Geometry--Topology Graph Priors through Boundary-Constrained Mixed Diffusion for Sparse-Slice 3D Porous Reconstruction

Diffusion-based voxel prior modelling is challenging for the reconstruction of large-scale 3D porous microstructures. Due to the demanding requirements for simultaneously modelling both the continuous pore morphology and the discrete pore-throat topology, the diffusion models require fully observed CT scans to provide topology-faithful priors, which results in an inherent trade-off among throughput, topological fidelity, and field of view in practical industrial applications. We propose GeoTopoDiff, a graph diffusion-based framework for reconstructing 3D porous microstructures from sparse CT slices. GeoTopoDiff transfers the learning of diffusion priors from a voxel-based space to a mixed graph state space, which simultaneously encompasses continuous pore geometry and discrete pore-throat topology. A topology-aware partial graph prior from sparsely observed CT slices is introduced to constrain the reverse denoising process. Experiments on anisotropic PTFE and Fontainebleau sandstone show that GeoTopoDiff reduces morphology-related errors by 19.8% and topology-sensitive transport errors by 36.5% on average. Our findings suggest that the mixed graph state space promotes the diffusion denoising process to reduce posterior uncertainty under a sparse observations. All models and code have been made publicly available to facilitate the exploration of diffusion models in the field of 3D porous microstructures simulation.

Yue Shi, Peng Wang, Mingzhe Yu +5

Manchester Metropolitan University, Manchester M1 5GD, U.K. · University of Surrey, Surrey, GU2 7XH, U.K. · Johnson Matthey Billingham, TS23 1LB, U.K. +1

3D Reconstruction Sparse-View CT Reconstruction Computed Tomography Graph Diffusion

Apr 30, 2026cs.CV

Residual Gaussian Splatting for Ultra Sparse-View CBCT Reconstruction

While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view conditions, leading to over-smoothing and a loss of high-frequency anatomical details. Since wavelet transforms provide rich high-frequency information and have been widely utilized to enhance sparse reconstruction, this work integrates wavelet multi-resolution analysis with 3DGS. To circumvent the mathematical mismatch between the strict non-negativity of physical X-ray attenuation and the bipolar nature of high-frequency wavelet coefficients, we propose Residual Gaussian Splatting (RGS). Methodologically, we introduce a spectrally-decoupled Gaussian representation that stratifies the volumetric field into a geometric base component and a residual detail component. This decomposition systematically transforms explicit high-frequency fitting into a physically consistent, implicit residual compensation task. Furthermore, we devise a spectral-spatial collaborative optimization strategy to coordinate the interplay between geometric anchoring and texture refinement, effectively preventing spectral crosstalk. Extensive experiments on clinical datasets demonstrate that RGS enables the reconstructed images to capture highly refined geometric textures. It successfully resolves the trade-off between artifact suppression and detail preservation, yielding superior visual fidelity in complex trabecular and vascular structures compared to existing neural rendering baselines.

Jian Lin, Jiancheng Fang, Shaoyu Wang +4

School of Information Engineering, Nanchang University, Nanchang 330031, China · Laboratory of Image Science and Technology, the School of Computer Science and Engineering, and the Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, Southeast University, Nanjing 210096, China

3D Gaussian Splatting Cone-Beam CT Sparse-View CT Reconstruction

Apr 23, 2026eess.IV

Conditional Diffusion Posterior Alignment for Sparse-View CT Reconstruction

Computed Tomography (CT) is a widely used imaging modality in medical and industrial applications. To limit radiation exposure and measurement time, there is a growing interest in sparse-view CT, where the number of projection views is significantly reduced. Deep neural networks have shown great promise in improving reconstruction quality in sparse-view CT, especially generative diffusion models. However, these methods struggle to scale to large 3D volumes due to several reasons: (i) the high memory and computational requirements of 3D models, (ii) the lack of large 3D training datasets, and (iii) the inconsistencies across slices when using 2D models independently on each slice. We overcome these limitations and scale diffusion-based sparse-view CT reconstruction to large 3D volumes by combining conditional diffusion with explicit data consistency. We propose Conditional Diffusion Posterior Alignment (CDPA) to enable scalable 3D sparse-view CT reconstruction. A 2D U-Net diffusion model is conditioned on an initial 3D reconstruction to improve inter-slice consistency, combined with data-consistency alignment to match measured projections. Experiments on synthetic and real Cone Beam CT (CBCT) data show state-of-the-art performance, with ablations that confirm the synergistic effects of the proposed pipeline. Finally, we show that the same principles also strengthen fast denoising U-Nets, yielding near-diffusion quality at a fraction of the computational cost.

Luis Barba, Johannes Kirschner, Benjamin Bejar

Swiss Data Science Center (SDSC) in Paul Scherrer Institute (PSI), Villigen, Switzerland. · Swiss Data Science Center (SDSC) and ETH Zurich, Switzerland. · Swiss Data Science Center (SDSC) and Paul Scherrer Institute (PSI), Villigen, Switzerland.

Cone-Beam CT 3D Medical Imaging Sparse-View CT Reconstruction Conditional Diffusion Models Diffusion Posterior Sampling

Apr 23, 2026eess.IV

DiffNR: Diffusion-Enhanced Neural Representation Optimization for Sparse-View 3D Tomographic Reconstruction

Neural representations (NRs), such as neural fields and 3D Gaussians, effectively model volumetric data in computed tomography (CT) but suffer from severe artifacts under sparse-view settings. To address this, we propose DiffNR, a novel framework that enhances NR optimization with diffusion priors. At its core is SliceFixer, a single-step diffusion model designed to correct artifacts in degraded slices. We integrate specialized conditioning layers into the network and develop tailored data curation strategies to support model finetuning. During reconstruction, SliceFixer periodically generates pseudo-reference volumes, providing auxiliary 3D perceptual supervision to fix underconstrained regions. Compared to prior methods that embed CT solvers into time-consuming iterative denoising, our repair-and-augment strategy avoids frequent diffusion model queries, leading to better runtime performance. Extensive experiments show that DiffNR improves PSNR by 3.99 dB on average, generalizes well across domains, and maintains efficient optimization.

Shiyan Su, Ruyi Zha, Danli Shi +2

1Monash University · 2The Australian National University · 3Hong Kong Polytechnic University

Diffusion Models for Image Restoration Sparse-View CT Reconstruction Diffusion Model Fine-Tuning Computed Tomography

Apr 21, 2026cs.CV

Generative Drifting for Conditional Medical Image Generation

Conditional medical image generation plays an important role in many clinically relevant imaging tasks. However, existing methods still face a fundamental challenge in balancing inference efficiency, patient-specific fidelity, and distribution-level plausibility, particularly in high-dimensional 3D medical imaging. In this work, we propose GDM, a generative drifting framework that reformulates deterministic medical image prediction as a multi-objective learning problem to jointly promote distribution-level plausibility and patient-specific fidelity while retaining one-step inference. GDM extends drifting to 3D medical imaging through an attractive-repulsive drift that minimizes the discrepancy between the generator pushforward and the target distribution. To enable stable drifting-based learning in 3D volumetric data, GDM constructs a multi-level feature bank from a medical foundation encoder to support reliable affinity estimation and drifting field computation across complementary global, local, and spatial representations. In addition, a gradient coordination strategy in the shared output space improves optimization balance under competing distribution-level and fidelity-oriented objectives. We evaluate the proposed framework on two representative tasks, MRI-to-CT synthesis and sparse-view CT reconstruction. Experimental results show that GDM consistently outperforms a wide range of baselines, including GAN-based, flow-matching-based, and SDE-based generative models, as well as supervised regression methods, while improving the balance among anatomical fidelity, quantitative reliability, perceptual realism, and inference efficiency. These findings suggest that GDM provides a practical and effective framework for conditional 3D medical image generation.

Zirong Li, Siyuan Mei, Weiwen Wu +3

Department of Orthodontics and Orofacial Orthopedics, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany · Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany · Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany +1

3D Medical Imaging One-Step Generative Modeling Sparse-View CT Reconstruction Medical Image Synthesis Conditional Generation

Apr 17, 2026cs.CV

SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Markus Haltmeier, Lukas Neumann, Nadja Gruber +1

Self-Supervised Learning Sparse-View CT Reconstruction Computed Tomography Inverse Problems Image Inverse Problems

Mar 16, 2026cs.CV

ILV: Iterative Latent Volumes for Fast and Accurate Sparse-View CT Reconstruction

A long-term goal in CT imaging is to achieve fast and accurate 3D reconstruction from sparse-view projections, thereby reducing radiation exposure, lowering system cost, and enabling timely imaging in clinical workflows. Recent feed-forward approaches have shown strong potential toward this overarching goal, yet their results still suffer from artifacts and loss of fine details. In this work, we introduce Iterative Latent Volumes (ILV), a feed-forward framework that integrates data-driven priors with classical iterative reconstruction principles to overcome key limitations of prior feed-forward models in sparse-view CBCT reconstruction. At its core, ILV constructs an explicit 3D latent volume that is repeatedly updated by conditioning on multi-view X-ray features and the learned anatomical prior, enabling the recovery of fine structural details beyond the reach of prior feed-forward models. In addition, we develop and incorporate several key architectural components, including an X-ray feature volume, group cross-attention, efficient self-attention, and view-wise feature aggregation, that efficiently realize its core latent volume refinement concept. Extensive experiments on a large-scale dataset of approximately 14,000 CT volumes demonstrate that ILV significantly outperforms existing feed-forward and optimization-based methods in both reconstruction quality and speed. These results show that ILV enables fast and accurate sparse-view CBCT reconstruction suitable for clinical use. The project page is available at: https://sngryonglee.github.io/ILV/.

Seungryong Lee, Woojeong Baek, Joosang Lee +1

Sungkyunkwan University · Yonsei University

Cone-Beam CT Image Reconstruction Sparse-View CT Reconstruction Feed-Forward 3D Reconstruction

Mar 6, 2026cs.CV

Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction

Sparse-view computed tomography (CT) is critical for reducing radiation exposure to patients. Recent advances in radiative 3D Gaussian Splatting (3DGS) have enabled fast and accurate sparse-view CT reconstruction. Despite these algorithmic advancements, practical reconstruction fidelity remains fundamentally bounded by the quality of the captured data, raising the crucial yet underexplored problem of X-ray active view selection. Existing active view selection methods are primarily designed for natural-light scenes and fail to capture the unique geometric ambiguities and physical attenuation properties inherent in X-ray imaging. In this paper, we present Perturbed Gaussian Ensemble, an active view selection framework that integrates uncertainty modeling with sequential decision-making, tailored for X-ray Gaussian Splatting. Specifically, we identify low-density Gaussian primitives that are likely to be uncertain and apply stochastic density scaling to construct an ensemble of plausible Gaussian density fields. For each candidate projection, we measure the structural variance of the ensemble predictions and select the one with the highest variance as the next best view. Extensive experimental results on arbitrary-trajectory CT benchmarks demonstrate that our density-guided perturbation strategy effectively eliminates geometric artifacts and consistently outperforms existing baselines in progressive tomographic reconstruction under unified view selection protocols.

Yulun Wu, Ruyi Zha, Wei Cao +3

University of Illinois Urbana-Champaign · Australian National University · Johns Hopkins University

3D Gaussian Splatting Active Perception Sparse-View CT Reconstruction Active View Selection

Feb 27, 2026eess.IV

Efficient Flow Matching for Sparse-View CT Reconstruction

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

Jiayang Shi, Lincen Yang, Zhong Li +3

Centrum Wiskunde en Informatica · LIACS, Leiden University · Great Bay University +1

Flow Matching Sparse-View CT Reconstruction Computational Imaging Computed Tomography

Feb 9, 2026cs.CV

Artifact Reduction in Undersampled 3D Cone-Beam CTs using a Hybrid 2D-3D CNN Framework

Undersampled CT volumes minimize acquisition time and radiation exposure but introduce artifacts degrading image quality and diagnostic utility. Reducing these artifacts is critical for high-quality imaging. We propose a computationally efficient hybrid deep-learning framework that combines the strengths of 2D and 3D models. First, a 2D U-Net operates on individual slices of undersampled CT volumes to extract feature maps. These slice-wise feature maps are then stacked across the volume and used as input to a 3D decoder, which utilizes contextual information across slices to predict an artifact-free 3D CT volume. The proposed two-stage approach balances the computational efficiency of 2D processing with the volumetric consistency provided by 3D modeling. The results show substantial improvements in inter-slice consistency in coronal and sagittal direction with low computational overhead. This hybrid framework presents a robust and efficient solution for high-quality 3D CT image post-processing. The code of this project can be found on github: https://github.com/J-3TO/2D-3DCNN_sparseview/.

Johannes Thalhammer, Tina Dorosti, Sebastian Peterhansl +3

Chair of Biomedical Physics, Department of Physics, School of Natural Sciences · Munich Institute of Biomedical Engineering · Institute for Diagnostic and Interventional Radiology, School of Medicine and Health, TUM Klinikum +2

Cone-Beam CT Sparse-View CT Reconstruction Convolutional Neural Networks Computed Tomography