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REVIEW 4 major objections 5 minor 57 references

Integrating Data and Image Domain Deep Learning for Limited Angle Tomography using Consensus Equilibrium

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A consensus-equilibrium framework fuses data-domain and image-domain deep learning for 90-degree limited-angle CT, and on real security CT slices it beats all six methods compared.

desk verdict A competent, useful applied paper that fuses data- and image-domain cGANs via consensus equilibrium for limited-angle CT; the gains are modest and the CE iteration is unverified past 4 steps, but it deserves a real review. read the letter →

arxiv 1909.00240 v1 pith:OXQXKQDJ submitted 2019-08-31 eess.IV cs.CVcs.LG

Muhammad Usman Ghani , W. Clem Karl This is my paper · ORCID
classification eess.IVcs.CVcs.LG
keywords limited-angleCTconsensusequilibriumdeeplearningreconstructionconditionalgenerativeadversarialnetworkssinogramcompletionimagepost-processingsecuritydataconsistency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that limited-angle CT reconstruction improves when deep learning is applied on both sides of the reconstruction: a conditional GAN first completes the missing projection data, a second conditional GAN then refines the reconstructed image, and a consensus-equilibrium (CE) mechanism holds the two agents together instead of training them end to end. The authors argue that image-only post-processing cannot recover structure lost by filtered backprojection, while data-only completion leaves residual artifacts, so the two should be fused with the CT physics model. On a real 90-degree limited-angle security CT test set, the proposed DICE approach achieves the best RMSE (73 HU), PSNR (26.55 dB), and SSIM (0.81) among the six methods compared. If the approach holds, it offers a template for combining learned priors with physical forward models in other limited-data tomographic settings.

What carries the argument

The central object is the consensus-equilibrium (CE) fixed-point formulation, which treats the CT data-consistency step and the trained image-enhancement network as two agents that must agree on a common image $x^*$. The data agent solves $F_{\text{data}}(v_1) = \arg\min_{x\ge 0} \frac{1}{2}\|\hat{y}_{\text{consistent}} - Ax\|_W^2 + \frac{1}{2\sigma^2}\|v_1-x\|_2^2$, where $\hat{y}_{\text{consistent}}$ is the completed projection data re-projected through the CT system matrix $A$; the image agent is simply $F_{\text{image}}(v_2)=\varphi_{\text{image}}(v_2)$, the trained cGAN. The CE equations require $F_{\text{data}}(v_1^*)=x^*$, $F_{\text{image}}(v_2^*)=x^*$, and $\mu_1 u_1^*+\mu_2 u_2^*=0$ with $x^*=\mu_1 v_1^*+\mu_2 v_2^*$, so the algorithm seeks a fixed point of $T=(2F-I)(2G-I)$ via Mann iterations. The paper uses four outer iterations, $\rho=0.25$, $\mu_1=0.6$, $\mu_2=0.4$, and 20 conjugate-gradient steps inside the data agent.

What would settle it

Re-run DICE on the same 315-slice test set with 1, 2, 4, 8, and 16 outer CE iterations, holding the networks, weights, and initialization fixed; if the RMSE/PSNR/SSIM curves do not stabilize by 4 iterations, the reported advantage is a stopping-rule artifact rather than evidence of consensus.

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Extended reading notes

Core claim

The central claim is that a consensus-equilibrium framework can integrate a data-domain cGAN that completes limited-angle sinograms and an image-domain cGAN that enhances patch-based image quality, producing reconstructions that outperform either network used alone. The data agent does not use the cGAN output directly: completed projections are re-projected through the CT forward model to enforce consistency, and the resulting consistent data is fed into a weighted data-fidelity term; the image agent maps images toward the learned prior. CE then finds an image that balances the two agents through a fixed-point iteration. On 315 slices from a real security CT dataset, DICE reports RMSE 73 HU, PSNR 26.55 dB, and SSIM 0.81, better than FBP, FBP plus post-processing, data completion followed by FBP with or without post-processing, and MBIR initialized with the same completed data. The authors present this as a demonstration that combining data-domain and image-domain deep learning through CE can outperform existing post-processing methods on a real limited-angle security problem.

Load-bearing premise

The load-bearing premise is that four steps of the consensus-equilibrium iteration land close enough to a true consensus that the reported gains come from the balanced fusion itself, rather than from the chosen stopping point, weights, or initialization.

Editorial extensions

If this is right

  • If DICE's claim holds, limited-angle scans from non-rotating security gantries can be reconstructed with much lower artifacts than FBP or image post-processing alone, recovering both missing structure and CT-number uniformity.
  • The same two-agent CE scaffold can be reused with different learned data and image networks, so future improvements in either cGAN should carry directly into the fused reconstruction.
  • Data consistency is part of the winning recipe: the completed data entering the physics agent is the re-projected, consistent estimate $\hat{y}_{\text{consistent}}$, not the raw cGAN output, and the authors report this improves results.
  • Because the image-domain network is trained against full-view MBIR reconstructions, DICE's reported quality is measured relative to that MBIR reference rather than to an absolute truth.
  • The authors state the same framework can be applied to other limited-data problems such as electron microscopy, non-destructive evaluation, and medical imaging; if the mechanism generalizes, those fields gain a template for fusing learned priors with physics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural stress test beyond the reported experiments is to vary the CE outer-iteration count (1, 2, 4, 8, and 16) on the same test set; if quality does not stabilize by 4 iterations, the reported margin may be a stopping-rule artifact rather than evidence of consensus.
  • A likely extension, which the authors flag as ongoing work, is to make the data-domain network a third CE agent instead of a fixed front-end, letting completion errors be corrected during fusion rather than locked in before reconstruction.
  • A testable prediction is that the fusion gain will shrink or vanish if the consistency re-projection is removed or if the completed sinogram is corrupted, since the data agent's data-fidelity term depends entirely on $\hat{y}_{\text{consistent}}$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes DICE, a consensus equilibrium (CE) framework that integrates a data-domain deep learning (cGAN-based sinogram completion) agent with an image-domain deep learning (cGAN-based image enhancement) agent for limited-angle CT reconstruction. The data agent combines the completed projection data with a CT physics model via an MBIR-type data fidelity term; the image agent is a learned patch-based prior. The two agents are combined through the CE fixed-point equations and solved with Mann iterations, limited to four outer iterations. Experiments on a real security CT dataset with 90-degree limited-angle data show that DICE achieves the lowest RMSE, highest PSNR, and highest SSIM among the considered methods (FBP, FBP+post-processing, data completion alone and with post-processing, and MBIR initialized with the same data).

Significance. If the central claim holds, the paper provides a practical way to combine data-domain and image-domain deep learning within a principled multi-agent reconstruction framework, with demonstrated gains on a real, challenging limited-angle security CT problem. The use of the same initialization and completed data for the DICE and MBIR baselines is a strength of the experimental design, and the inclusion of real CT data with multiple baseline methods adds value. However, the significance of the contribution is currently limited by two load-bearing gaps: the CE iteration is not shown to converge (the algorithm fixes the number of iterations at four), and the definition of the consistent projection data used by the data-fidelity agent is internally inconsistent between the method description and the algorithm. These issues must be resolved before the claim that DICE outperforms alternatives 'using CE framework' can be accepted. The reported gains over the closest baseline are modest, and no error bars or significance tests are provided, so the statistical robustness of the claim is also open.

major comments (4)
  1. [Section 3.3 and Algorithm 1] The CE solution is defined as a fixed point of the map T=(2F-I)(2G-I), but the Mann iteration in Eq. (9) is stopped after exactly four outer iterations, with the text stating only that this 'was observed to be adequate' and deferring convergence analysis. Since the image agent F_image is a trained cGAN, no nonexpansiveness or other contraction property of T is established. The reported DICE result is therefore not verified to be a CE solution; it may be a fixed-budget heuristic whose advantage over 'Initialization + MBIR' depends on the stopping rule, the Mann parameter rho, and the weights mu1/mu2. The authors should report the evolution of the CE residual (e.g., ||z^(k+1)-z^(k)|| or the distance to the fixed-point equations) over iterations, run more than four iterations for at least a subset of test slices, and either establish convergence conditions or explicitly frame the contribution as a fixed-budget algorithm rather than a converged CE solution.
  2. [Algorithm 1, step 2 vs. Section 3.1] There is a direct inconsistency in the definition of the consistent projection data. Section 3.1 and Eq. (4) define y_consistent = A * FBP(y_complete), but Algorithm 1 sets y_consistent = A * x^(0), where x^(0) = phi_image(FBP(y_complete)) is the image-domain-enhancement output. If the implementation follows the algorithm, then the data-fidelity agent in Eq. (5) is fitting a quantity derived from the image enhancement, not from the data-domain completion as described. This weakens the anchor to the measured limited-angle data and could make the 'Initialization + MBIR' baseline circular, since it fits the same re-projected enhanced image. The authors must clarify which definition is actually used, correct the discrepancy, and if the algorithm version is intended, justify why the data consistency term should target a reprojection of the image-enhanced initialization.
  3. [Table 1] The quantitative comparison reports only average RMSE, PSNR, and SSIM over the test slices, without error bars, standard deviations, or statistical significance tests. The margins over the closest baseline (Initialization + MBIR) are small (RMSE 73 vs 76 HU, PSNR 26.55 vs 26.14 dB, SSIM 0.81 vs 0.78). To support the claim that DICE 'outperforms all the considered methods on all three metrics,' the authors should report per-slice variability, paired differences, and ideally a significance test or confidence intervals.
  4. [Section 4 and Table 1] The ground truth used for both training the image-domain cGAN and for quantitative evaluation consists of full-view MBIR reconstructions. Since the image-domain network is trained to map low-quality images to these same MBIR targets, the reported metrics partly measure how closely each method reproduces the chosen MBIR reference rather than the true object. This is a limitation that should be discussed, and the evaluation would be strengthened by additional metrics or a comparison on data where a non-MBIR ground truth is available.
minor comments (5)
  1. [Abstract and Figure 1 captions] The text repeatedly renders the angle as '900' (e.g., 'challenging 900 limited-angle problem'); this should be '90°'.
  2. [Algorithm 1] The algorithm uses '← −' in several assignments (e.g., 'z(0)← −[x(0);x(0)]', 'k← −0'), which appears to be a formatting artifact; the minus signs should be removed if not intended.
  3. [Section 3.1] There are minor typos such as 'transponsed' for 'transposed' in the architecture description; these should be corrected.
  4. [Section 4.1] The 'Initialization + MBIR' baseline is described as using '4 iterations of MBIR', but the MBIR objective, regularization, and stopping criterion are not specified; this information should be provided for reproducibility.
  5. [Section 5] The abstract and introduction mention 'efficient computation' as a benefit of the proposed approach, but no runtime or computational cost comparison is reported; adding this would substantiate the claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the derivation chain is an empirical application of an external CE framework to two independently trained cGANs; the stated 4-iteration convergence caveat is a correctness risk, not a circular reduction.

full rationale

The claimed result is an empirical comparison, not a derivation from first principles. The CE equations (1)-(3) and the Mann iteration (9) are taken from the published consensus-equilibrium framework [9,50], and the paper does not present them as its own derivation; citing an external framework is not circular. The data-domain cGAN (Section 3.1) and image-domain cGAN (Section 3.2) are trained on a separate 168-bag training split and applied to 21 held-out test bags, with the image cGAN trained against full-view MBIR references while test metrics also use full-view MBIR references; this is a shared benchmark convention for all compared DL methods and does not make the DICE output equal to any fitted input by construction. The self-citations [38,53] are used for architectural inspiration and for the cGAN training schedule, but the networks are re-trained and evaluated here, so the citations are not load-bearing in the sense of substituting for evidence. The one explicitly flagged limitation is in Section 3.3: 'we simply limit the number of outer iterations to 4, which was observed to be adequate. Further work on convergence analysis will be conducted in the future.' This means the reported image is not verified to be the CE fixed point, so the label 'consensus equilibrium solution' is heuristic; however, a missing convergence proof is an epistemic and correctness concern, not a circular definition. The 4-iteration output is not, by the paper's own equations, equal to the CE fixed point by construction. No fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' prior work. Therefore no significant circularity is present.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The DICE framework rests on the CT forward model, the choice of full-view MBIR as ground truth, the transfer of CE theory to DNN agents, and a set of hyperparameters (lambda, sigma2, rho, mu, iteration counts) that are chosen empirically. No new physical entities are introduced. The largest unverified item is the convergence of the Mann iteration with cGAN agents.

free parameters (8)
  • lambda_data = 100
    Pixel-loss weight in data-domain cGAN objective, empirically selected in Section 4.
  • lambda_image = 1e-5
    Pixel-loss weight in image-domain cGAN objective, empirically selected in Section 4.
  • sigma2_CE = 1e-8
    Trade-off parameter in the data-fidelity CE agent, Eq. (5).
  • rho_Mann = 0.25
    Step size in Mann iterations, Eq. (9).
  • mu1_mu2 = mu1=0.6, mu2=0.4
    Agent combination weights in CE averaging, Eq. (3) and Algorithm 1.
  • num_CE_iterations = 4
    Number of outer CE iterations, chosen because 'observed to be adequate' in Section 3.3.
  • CG_iterations_data_agent = 20
    Inner conjugate-gradient iterations used to apply the data agent, Section 3.3.
  • CG_iterations_image_training = 40
    Conjugate-gradient iterations used to generate low-quality training images for the image cGAN, Section 4.
assumptions (4)
  • domain assumption The parallel-beam forward projection operator A and FBP provide a valid approximate CT model for the rebinned security data.
    Used in Eq. (4)-(5) and Algorithm 1 to impose projection consistency.
  • domain assumption Full-view MBIR reconstructions are treated as ground truth for training and evaluation.
    Image cGAN is trained on full-view MBIR patches and Table 1 scores against full-view MBIR; if MBIR is biased, all comparisons share that bias.
  • ad hoc to paper CE fixed-point theory from [9,50] applies to the DNN-based agents.
    The agents Fdata and Fimage include trained cGANs; the paper limits to 4 Mann iterations and defers convergence analysis.
  • standard math Standard optimization and training assumptions for cGANs and Adam hold.
    Training uses standard GAN/optimization machinery; no novel mathematical framework is introduced.

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Cite this review

Pith. "Pith review of Integrating Data and Image Domain Deep Learning for Limited Angle Tomography using Consensus Equilibrium." pith.science (2026). https://pith.science/paper/OXQXKQDJ

@misc{pith2026190900240,
  author       = {Pith},
  title        = {Pith review of: Integrating Data and Image Domain Deep Learning for Limited Angle Tomography using Consensus Equilibrium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OXQXKQDJ}},
  note         = {Machine review of arXiv:1909.00240}
}
read the original abstract

Computed Tomography (CT) is a non-invasive imaging modality with applications ranging from healthcare to security. It reconstructs cross-sectional images of an object using a collection of projection data collected at different angles. Conventional methods, such as FBP, require that the projection data be uniformly acquired over the complete angular range. In some applications, it is not possible to acquire such data. Security is one such domain where non-rotational scanning configurations are being developed which violate the complete data assumption. Conventional methods produce images from such data that are filled with artifacts. The recent success of deep learning (DL) methods has inspired researchers to post-process these artifact laden images using deep neural networks (DNNs). This approach has seen limited success on real CT problems. Another approach has been to pre-process the incomplete data using DNNs aiming to avoid the creation of artifacts altogether. Due to imperfections in the learning process, this approach can still leave perceptible residual artifacts. In this work, we aim to combine the power of deep learning in both the data and image domains through a two-step process based on the consensus equilibrium (CE) framework. Specifically, we use conditional generative adversarial networks (cGANs) in both the data and the image domain for enhanced performance and efficient computation and combine them through a consensus process. We demonstrate the effectiveness of our approach on a real security CT dataset for a challenging 90 degree limited-angle problem. The same framework can be applied to other limited data problems arising in applications such as electron microscopy, non-destructive evaluation, and medical imaging.

Figures

Figures reproduced from arXiv: 1909.00240 by the authors.

Figure 1
Figure 1. FBP and proposed DICE method reconstructions using [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of our DICE framework is presented. Data [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Overall architecture of our data completion cGAN is presented. The abbreviated legends in the Figure are defined here; Conv: [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Overall architecture of our image-domain cGAN is presented. It learns patch-based image priors from a large security dataset. The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Data completion results are presented along with ref [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Limited angle CT reconstruction results using different methods are presented. Here DC refers to data domain cGAN based [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Reference graph

Works this paper leans on

57 extracted references · 53 canonical work pages

  1. [1]

    Statistical image reconstruction for polyenergetic X-ray computed tomogra- phy,

    Elbakri, Idris A and Fessler, Jeffrey A, “Statistical image reconstruction for polyenergetic X-ray computed tomogra- phy,”IEEE transactions on medical imaging, vol. 21, no. 2, pp. 89–99, 2002

    work page 2002

  2. [2]

    Modeling and pre-treatment of photon- starved CT data for iterative reconstruction,

    Chang, Zhiqian and Zhang, Ruoqiao and Thibault, Jean- Baptiste and Pal, Debashish and Fu, Lin and Sauer, Ken and Bouman, Charles, “Modeling and pre-treatment of photon- starved CT data for iterative reconstruction,” IEEE transac- tions on medical imaging, vol. 36, no. 1, pp. 277–287, 2017

    work page 2017

  3. [3]

    Variable splitting techniques for discrete tomography,

    Tuysuzoglu, Ahmet and Khoo, Yuehaw and Karl, W Clem, “Variable splitting techniques for discrete tomography,” in Image Processing (ICIP), 2016 IEEE International Confer- ence on. IEEE, 2016, pp. 1764–1768

    work page 2016

  4. [4]

    TIMBIR: A Method for Time-Space Reconstruc- tion from Interlaced Views,

    K. A. Mohan, S. Venkatakrishnan, J. W. Gibbs, E. B. Gul- soy, X. Xiao, M. De Graef, P. W. V oorhees, and C. A. Bouman, “TIMBIR: A Method for Time-Space Reconstruc- tion from Interlaced Views,” IEEE Transactions on Compu- tational Imaging, vol. 1, no. 2, pp. 96–111, 2015

    work page 2015

  5. [5]

    Carmignato, W

    S. Carmignato, W. Dewulf, and R. Leach, Industrial X-ray computed tomography. Springer, 2018

    work page 2018

  6. [6]

    Learning-Based Object Identification and Segmentation Using Dual-Energy CT Images for Se- curity,

    Martin, Limor and Tuysuzoglu, Ahmet and Karl, W Clem and Ishwar, Prakash, “Learning-Based Object Identification and Segmentation Using Dual-Energy CT Images for Se- curity,” IEEE Transactions on Image Processing , vol. 11, no. 24, pp. 4069–4081, 2015

    work page 2015

  7. [7]

    Deep learning based sinogram correction for metal artifact reduction,

    M. U. Ghani and W. C. Karl, “Deep learning based sinogram correction for metal artifact reduction,” Electronic Imaging, no. XVI, pp. 472–1 – 472–8, 2018

    work page 2018

  8. [8]

    A Model-Based Image Reconstruction Algorithm With Simultaneous Beam Hardening Correction for X-Ray CT

    Jin, Pengchong and Bouman, Charles A and Sauer, Ken D, “A Model-Based Image Reconstruction Algorithm With Simultaneous Beam Hardening Correction for X-Ray CT.” IEEE Trans. Computational Imaging, vol. 1, no. 3, pp. 200– 216, 2015

    work page 2015

Show all 57 references
  1. [9]

    Plug-and-play unplugged: Optimization-free reconstruc- tion using consensus equilibrium,

    G. T. Buzzard, S. H. Chan, S. Sreehari, and C. A. Bouman, “Plug-and-play unplugged: Optimization-free reconstruc- tion using consensus equilibrium,”SIAM Journal on Imaging Sciences, vol. 11, no. 3, pp. 2001–2020, 2018

    2001

  2. [10]

    Improved total variation-based CT image reconstruc- tion applied to clinical data,

    L. Ritschl, F. Bergner, C. Fleischmann, and M. Kachel- rieß, “Improved total variation-based CT image reconstruc- tion applied to clinical data,”Physics in Medicine & Biology, vol. 56, no. 6, p. 1545, 2011

    2011

  3. [11]

    A Gaussian mixture MRF for model-based iterative reconstruction with applications to low-dose X-ray CT,

    R. Zhang, D. H. Ye, D. Pal, J.-B. Thibault, K. D. Sauer, and C. A. Bouman, “A Gaussian mixture MRF for model-based iterative reconstruction with applications to low-dose X-ray CT,” IEEE Transactions on Computational Imaging, vol. 2, no. 3, pp. 359–374, 2016

    2016

  4. [12]

    Deep Resid- ual Learning for Model-Based Iterative CT Reconstruction using Plug-and-Play Framework,

    Ye, Dong Hye and Srivastava, Somesh and Thibault, Jean- Baptiste and Sauer, Ken and Bouman, Charles, “Deep Resid- ual Learning for Model-Based Iterative CT Reconstruction using Plug-and-Play Framework,” in 2018 IEEE Interna- tional Conference on Acoustics, Speech and Signal Pr...

    2018

  5. [13]

    Coherent-Image Reconstruction Using Convolutional Neu- ral Networks,

    C. J. PeUizzari, M. F. Spencer, and C. A. Bouman, “Coherent-Image Reconstruction Using Convolutional Neu- ral Networks,” inMathematics in Imaging. Optical Society of America, 2019, pp. MTu4D–4

    2019

  6. [14]

    Image-to-Image Translation with Conditional Adversarial Networks,

    P. Isola and J. Y . Zhu and T. Zhou and A. A. Efros, “Image-to-Image Translation with Conditional Adversarial Networks,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017-07, pp. 5967–5976

    2017

  7. [15]

    Motion-compensated image reconstruction for cardiac CT with sinogram-based motion estimation,

    J. H. Cho and J. A. Fessler, “Motion-compensated image reconstruction for cardiac CT with sinogram-based motion estimation,” in 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC). IEEE, 2013, pp. 1–5

    2013

  8. [16]

    Fast and robust discrete computational imaging,

    A. Tuysuzoglu, Y . Khoo, and W. C. Karl, “Fast and robust discrete computational imaging,” Electronic Imaging, vol. 2017, no. 17, pp. 49–54, 2017

    2017

  9. [17]

    Practical model 3DX of limited cone-beam X-ray CT for dental use,

    Y . Arai, K. Honda, K. Iwai, and K. Shinoda, “Practical model 3DX of limited cone-beam X-ray CT for dental use,” in In- ternational Congress Series, vol. 1230. Elsevier, 2001, pp. 713–718

    2001

  10. [18]

    Digital tomosynthesis in breast imaging,

    L. T. Niklason, B. T. Christian, L. E. Niklason, D. B. Kopans, D. E. Castleberry, B. Opsahl-Ong, C. E. Landberg, P. J. Slan- etz, A. A. Giardino, R. Moore et al., “Digital tomosynthesis in breast imaging,” Radiology, vol. 205, no. 2, pp. 399–406, 1997

    1997

  11. [19]

    Imagenet classification with deep convolutional neural networks,

    Krizhevsky, Alex and Sutskever, Ilya and Hinton, Geoffrey E, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, 2012, pp. 1097–1105

    2012

  12. [20]

    Image de- noising and inpainting with deep neural networks,

    Xie, Junyuan and Xu, Linli and Chen, Enhong, “Image de- noising and inpainting with deep neural networks,” in Ad- vances in Neural Information Processing Systems, 2012, pp. 341–349

    2012

  13. [21]

    Mask-specific inpainting with deep neural networks,

    K ¨ohler, Rolf and Schuler, Christian and Sch¨olkopf, Bernhard and Harmeling, Stefan, “Mask-specific inpainting with deep neural networks,” in German Conference on Pattern Recog- nition. Springer, 2014, pp. 523–534

    2014

  14. [22]

    Ac- curate image super-resolution using very deep convolutional networks,

    Kim, Jiwon and Kwon Lee, Jung and Mu Lee, Kyoung, “Ac- curate image super-resolution using very deep convolutional networks,” in Proceedings of the IEEE Conference on Com- puter Vision and Pattern Recognition, 2016, pp. 1646–1654

    2016

  15. [23]

    Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,

    Zhang, Kai and Zuo, Wangmeng and Chen, Yunjin and Meng, Deyu and Zhang, Lei, “Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,” IEEE Transactions on Image Processing, 2017

    2017

  16. [24]

    Loss functions for image restoration with neural networks,

    Zhao, Hang and Gallo, Orazio and Frosio, Iuri and Kautz, Jan, “Loss functions for image restoration with neural networks,” IEEE Transactions on Computational Imaging , vol. 3, no. 1, pp. 47–57, 2017

    2017

  17. [25]

    Can fully convolu- tional networks perform well for general image restoration problems?

    Chaudhury, Subhajit and Roy, Hiya, “Can fully convolu- tional networks perform well for general image restoration problems?” in Machine Vision Applications (MVA), 2017 Fifteenth IAPR International Conference on. IEEE, 2017, pp. 254–257

    2017

  18. [26]

    Advances in automatic target recognition (ATR) for CT based object detection system–Final report, Dept,

    Crawford, C, “Advances in automatic target recognition (ATR) for CT based object detection system–Final report, Dept,” Homeland Security Center Excellence, Task order number HSHQDC–12–J–00429, Boston, MA, 2014

    2014

  19. [27]

    Image recon- struction: From sparsity to data-adaptive methods and ma- chine learning,

    S. Ravishankar, J. C. Ye, and J. A. Fessler, “Image recon- struction: From sparsity to data-adaptive methods and ma- chine learning,”arXiv preprint arXiv:1904.02816, 2019

    1904 arXiv

  20. [28]

    Image prediction for limited-angle tomography via deep learning with convolutional neural network,

    H. Zhang, L. Li, K. Qiao, L. Wang, B. Yan, L. Li, and G. Hu, “Image prediction for limited-angle tomography via deep learning with convolutional neural network,” arXiv preprint arXiv:1607.08707, 2016

    2016 arXiv

  21. [29]

    Multi-scale wavelet domain residual learning for limited-angle CT reconstruction,

    J. Gu and J. C. Ye, “Multi-scale wavelet domain residual learning for limited-angle CT reconstruction,”arXiv preprint arXiv:1703.01382, 2017

    2017 arXiv

  22. [30]

    A sinogram inpainting method based on gen- erative adversarial network for limited-angle computed to- mography,

    Z. Li, W. Zhang, L. Wang, A. Cai, N. Liang, B. Yan, and L. Li, “A sinogram inpainting method based on gen- erative adversarial network for limited-angle computed to- mography,” in 15th International Meeting on Fully Three- Dimensional Image Reconstruction in Radiology and Nu- ...

    2019

  23. [31]

    Lose The Views: Limited Angle CT Recon- struction via Implicit Sinogram Completion,

    Anirudh, Rushil and Kim, Hyojin and Thiagarajan, Jayara- man J and Mohan, K Aditya and Champley, Kyle and Bre- mer, Timo, “Lose The Views: Limited Angle CT Recon- struction via Implicit Sinogram Completion,” arXiv preprint arXiv:1711.10388, 2017

    2017 arXiv

  24. [32]

    Deep learning computed tomography: Learning projection-domain weights from image domain in limited angle problems,

    T. W ¨urfl, M. Hoffmann, V . Christlein, K. Breininger, Y . Huang, M. Unberath, and A. K. Maier, “Deep learning computed tomography: Learning projection-domain weights from image domain in limited angle problems,” IEEE trans- actions on medical imaging , vol. 37, no. 6, pp. 145...

    2018

  25. [33]

    Deep convolutional neural net- work for inverse problems in imaging,

    Jin, Kyong Hwan and McCann, Michael T and Froustey, Em- manuel and Unser, Michael, “Deep convolutional neural net- work for inverse problems in imaging,” IEEE Transactions on Image Processing, vol. 26, no. 9, pp. 4509–4522, 2017

    2017

  26. [34]

    Low dose CT im- age denoising using a generative adversarial network with wasserstein distance and perceptual loss,

    Yang, Qingsong and Yan, Pingkun and Zhang, Yanbo and Yu, Hengyong and Shi, Yongyi and Mou, Xuanqin and Kalra, Mannudeep K and Wang, Ge, “Low dose CT im- age denoising using a generative adversarial network with wasserstein distance and perceptual loss,” arXiv preprint arXiv:17...

    2017 arXiv

  27. [35]

    Low-dose ct streak artifacts removal using deep residual neural network,

    Li, Heyi and Mueller, Klaus, “Low-dose ct streak artifacts removal using deep residual neural network,” inProceedings of Fully 3D conference, 2017, pp. 191–194

    2017

  28. [36]

    Framing U-Net via deep convolutional framelets: Application to sparse-view CT,

    Han, Yoseob and Ye, Jong Chul, “Framing U-Net via deep convolutional framelets: Application to sparse-view CT,” IEEE transactions on medical imaging , vol. 37, no. 6, pp. 1418–1429, 2018

    2018

  29. [37]

    Deep-Neural- Network-Based Sinogram Synthesis for Sparse-View CT Im- age Reconstruction,

    H. Lee, J. Lee, H. Kim, B. Cho, and S. Cho, “Deep-Neural- Network-Based Sinogram Synthesis for Sparse-View CT Im- age Reconstruction,” IEEE Transactions on Radiation and Plasma Medical Sciences, vol. 3, no. 2, pp. 109–119, 2018

    2018

  30. [38]

    Deep Learning-Based Sinogram Completion for Low-Dose CT,

    Ghani, Muhammad Usman and Karl, W Clem, “Deep Learning-Based Sinogram Completion for Low-Dose CT,” in 2018 IEEE 13th Image, Video, and Multidimensional Sig- nal Processing Workshop (IVMSP). IEEE, 2018, pp. 1–5

    2018

  31. [39]

    Sinogram interpola- tion for sparse-view micro-ct with deep learning neural net- work,

    X. Dong, S. Vekhande, and G. Cao, “Sinogram interpola- tion for sparse-view micro-ct with deep learning neural net- work,” in Medical Imaging 2019: Physics of Medical Imag- ing, vol. 10948. International Society for Optics and Pho- tonics, 2019, p. 109482O

    2019

  32. [40]

    Comparision of projection domain, image domain, and comprehensive deep learning for sparse-view X-ray CT image reconstruction,

    K. Liang, H. Yang, and Y . Xing, “Comparision of projection domain, image domain, and comprehensive deep learning for sparse-view X-ray CT image reconstruction,”arXiv preprint arXiv:1804.04289, 2018

    2018 arXiv

  33. [41]

    Image reconstruction by domain-transform manifold learn- ing,

    B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen, and M. S. Rosen, “Image reconstruction by domain-transform manifold learn- ing,”Nature, vol. 555, no. 7697, p. 487, 2018

    2018

  34. [42]

    Radon inversion via deep learning,

    J. He and J. Ma, “Radon inversion via deep learning,” in Medical Imaging 2019: Physics of Medical Imaging , vol. 10948. International Society for Optics and Photonics, 2019, p. 1094810

    2019

  35. [43]

    Plug-and-play priors for model based reconstruction,

    S. V . Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-play priors for model based reconstruction,” in 2013 IEEE Global Conference on Signal and Information Processing. IEEE, 2013, pp. 945–948

    2013

  36. [44]

    Plug-and-play priors for bright field electron tomography and sparse interpolation,

    S. Sreehari, S. V . Venkatakrishnan, B. Wohlberg, G. T. Buz- zard, L. F. Drummy, J. P. Simmons, and C. A. Bouman, “Plug-and-play priors for bright field electron tomography and sparse interpolation,” IEEE Transactions on Computa- tional Imaging, vol. 2, no. 4, pp. 408–423, 2016

    2016

  37. [45]

    Learning proximal operators: Using denoising networks for regularizing inverse imaging problems,

    T. Meinhardt, M. Moller, C. Hazirbas, and D. Cremers, “Learning proximal operators: Using denoising networks for regularizing inverse imaging problems,” in Proceedings of the IEEE International Conference on Computer Vision , 2017, pp. 1781–1790

    2017

  38. [46]

    Primal-dual plug-and-play image restoration,

    S. Ono, “Primal-dual plug-and-play image restoration,” IEEE Signal Processing Letters , vol. 24, no. 8, pp. 1108– 1112, 2017

    2017

  39. [47]

    A plug-and- play priors approach for solving nonlinear imaging inverse problems,

    U. S. Kamilov, H. Mansour, and B. Wohlberg, “A plug-and- play priors approach for solving nonlinear imaging inverse problems,” IEEE Signal Processing Letters, vol. 24, no. 12, pp. 1872–1876, 2017

    2017

  40. [48]

    Cnn-based projected gradient descent for consis- tent ct image reconstruction,

    H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consis- tent ct image reconstruction,” IEEE transactions on medical imaging, vol. 37, no. 6, pp. 1440–1453, 2018

    2018

  41. [49]

    The little engine that could: Regularization by denoising (RED),

    Y . Romano, M. Elad, and P. Milanfar, “The little engine that could: Regularization by denoising (RED),” SIAM Journal on Imaging Sciences, vol. 10, no. 4, pp. 1804–1844, 2017

    2017

  42. [50]

    Consensus equilibrium: A framework for model inte- gration,

    C. A. Bouman, G. T. Buzzard, and S. H. Chan, “Consensus equilibrium: A framework for model inte- gration,” in Imaging and Applied Optics 2018 (3D, AO, AIO, COSI, DH, IS, LACSEA, LS&C, MATH, pcAOP) . Optical Society of America, 2018, p. MW5D.1. [On- line]. Available: http://www...

    2018

  43. [51]

    Constrained sinogram restoration for limited-angle tomography,

    J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,”Optical Engineer- ing, vol. 29, no. 5, pp. 535–545, 1990

    1990

  44. [52]

    Generative ad- versarial nets,

    Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua, “Generative ad- versarial nets,” inAdvances in neural information processing systems, 2014, pp. 2672–2680

    2014

  45. [53]

    Fast Enhanced CT Metal Artifact Reduction using Data Do- main Deep Learning,

    Ghani, Muhammad Usman and Karl, W Clem, “Fast Enhanced CT Metal Artifact Reduction using Data Do- main Deep Learning,”IEEE Transactions on Computational Imaging, 2019

    2019

  46. [54]

    Tensorflow: Large-scale ma- chine learning on heterogeneous distributed systems,

    Abadi, Mart ´ın and Agarwal, Ashish and Barham, Paul and Brevdo, Eugene and Chen, Zhifeng and Citro, Craig and Corrado, Greg S and Davis, Andy and Dean, Jeffrey and Devin, Matthieu and others, “Tensorflow: Large-scale ma- chine learning on heterogeneous distributed systems,” ar...

    2016 arXiv

  47. [55]

    Fast and flexible X-ray tomography using the ASTRA toolbox,

    van Aarle, Wim and Palenstijn, Willem Jan and Cant, Jeroen and Janssens, Eline and Bleichrodt, Folkert and Dabravol- ski, Andrei and De Beenhouwer, Jan and Batenburg, K Joost and Sijbers, Jan, “Fast and flexible X-ray tomography using the ASTRA toolbox,” Optics express, vol. 24...

    2016

  48. [56]

    Adam: A method for stochastic optimization,

    Kingma, Diederik and Ba, Jimmy, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014

    2014 arXiv

  49. [57]

    Improved techniques for training gans,

    T. Salimans, I. Goodfellow, W. Zaremba, V . Cheung, A. Rad- ford, and X. Chen, “Improved techniques for training gans,” in Advances in neural information processing systems, 2016, pp. 2234–2242

    2016

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.