The DOI matches its Crossref record; 74 of the 83 references it cites were found in a registry or an index; none of the 13 sources its claims cite is checked for support yet.
Deep Convolutional Neural Network for Inverse Problems in Imaging
Open accessAbstract
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise nonlinearity) when the normal operator (H*H, where H* is the adjoint of the forward imaging operator, H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 × 512 image on the GPU.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper proposes FBPConvNet, a deep CNN that takes a filtered back projection (FBP) reconstruction as input and learns to remove artifacts for inverse problems whose normal operator is a convolution, demonstrated on sparse-view X-ray CT. It reports competitive or better SNR than TV-regularized iterative reconstruction on realistic synthetic and real CT datasets, with sub-second GPU reconstruction.
Key findings
- FBPConvNet outperformed TV-regularized iterative reconstruction on the biomedical synthetic dataset: at 143 views, SNR was 36.15 dB vs. 31.92 dB for TV; at 50 views, 28.83 dB vs. 25.20 dB.
- On the real experimental CT dataset, FBPConvNet also had higher SNR than TV: 11.34 dB vs. 8.25 dB at 145 views, and 8.85 dB vs. 7.25 dB at 14× subsampling (table lists 51 views).
- On the ellipsoidal synthetic dataset, TV outperformed FBPConvNet: 29.48 dB vs. 28.96 dB at 143 views, and 27.69 dB vs. 23.84 dB at 50 views; the paper attributes this to TV being optimal for piecewise-constant phantoms.
- Reconstruction speed was about 200 ms for FBP plus 200–300 ms for the CNN on GPU for a 512 × 512 image, versus around 7 minutes for iterative reconstruction; the abstract states less than one second total.
Methods
- Design: FBPConvNet applies discretized FBP to measurements, then a CNN based on U-net with multilevel decomposition, multichannel filtering, and residual learning via a skip connection; zero-padding is used and the final layer reduces 64 channels to a single output image. Training pairs low-view FBP images with full-view FBP images as input and output.
- Data: three datasets—ellipsoid synthetic (500 images, sinograms 729 × 1,000), biomedical synthetic (500 real in-vivo CT images from the Mayo Clinic Low-dose Grand Challenge, sinograms 729 × 1,000), and experimental real CT (377 sinograms from the TOMCAT beamline, each 1,493 × 721, from rat brain z-slices). Synthetic data used 475 training and 25 test images; real data used 327 training and 25 test images with a 25-slice gap. Subsampling was ×7 and ×20 for synthetic (143 and 50 views) and ×5 and ×14 for real (145 and 52 views).
- Analysis: SNR was the quantitative metric; FBP, TV-regularized iterative reconstruction [13], and FBPConvNet were compared. Training used MatConvNet, a Titan Black GPU, about 15 hours for 101 iterations, learning rate decreasing from 0.01 to 0.001, batch size 1, momentum 0.99, gradient clipping at 10⁻², and flip-flop augmentation. TV parameters were selected by golden-section search to optimize performance on the training set.
Limitations
- Stated: the method lacks transfer between datasets; a network trained on ×7 subsampled sinograms retained artifacts when applied to ×20 subsampled sinograms, and different dimensions or subsampling factors require retraining.
- Stated: the work focuses on X-ray CT; adapting to MRI or diffraction tomography is expected to be non-trivial experimentally, requiring large training sets and a high-quality iterative reconstruction for comparison, and complex-valued data would need a CNN architecture that correctly handles complex values.
- Evident/acknowledged: TV outperformed FBPConvNet on the ellipsoidal piecewise-constant phantom, which the paper says is reasonable because TV regularization should be optimal there; the paper also notes TV parameters were tuned on the training set rather than learned from data, and the correct way to learn such parameters remains open.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 13 cited sources checked · 0 supported · 0 flagged
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“requires less than a second to reconstruct a 512 × 512 image on the GPU.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In Figure 5, again, the sparse-view FBP contains line artifacts.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both the TV and FBPConvNet methods significantly reduce these artifacts, giving visually indistinguishable results.”
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This yields a noticeable increase in performance compared to the same network without the skip connection.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclear- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The average SNR on the testing set for the TV method is higher than that of the the FBPConvNet.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms.”
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: A twenty times reduction in the number of views corresponds to a twenty times reduction in the radiation dose received by the patient.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Especially, reconstructed images from the proposed network represented well complex textures which are important to diagnosis.”
Strength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A version of Theorem 1 also holds in the discrete case; we sketch the result here.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When the downsampling is increased to twenty times, Figure 4, the line artifacts in the sparse-view FBP reconstruction are even more pronounced.”
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
- It may state two separate claims as one. 20
- Probably not a substantial claim. 8
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 50 views (x20) | 8.44 | 27.69 | 23.84 |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the seven times downsampling case, Figure 3, the full-view FBP (ground truth) shows nearly artifact-free ellipsoids, while the sparseview FBP shows significant line artifacts (most visible in the background).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 143 views (x7) | 16.09 | 29.48 | 28.96 |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both the TV and FBPConvNet reduce these artifacts, though the FBPConvNet retains some of the artifacts.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When the forward model is normal-convolutional and when W is a convolution, the algorithm consists of iteratively filtering by I -(1 /L ) W ∗ H ∗ HW , adding a bias, (1 /L ) W ∗ H ∗ y , and applying a point-wise nonlinearity, S θ .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 50 views (x20) | 13.52 | 25.2 | 28.83 |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In Fig. 7, we observe the same trend as for the biomedical dataset, where the TV method oversmooths and the FBPConvNet better preserves fine structures.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is much faster than the iterative reconstruction, which, in our case, requires around 7 minutes even after the regularization parameters have been selected.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Furthermore, after training, the computation time of the proposed network per one image is under a second.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The conventional iterative algorithm with TV regularization outperformed the FBPConvNet in the ellipsoidal dataset, while the reverse was true for the biomedical and experimental datasets.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 145 views (x5) | 5.38 | 8.25 | 11.34 |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 143 views (x7) 24.97 | | 31.92 36.15 | |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both TV and the proposed method remove streaking artifacts satisfactorily; however, the TV reconstruction shows the cartoon-like artifacts that are typical of TV reconstructions.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| avg. SNR (dB) | 51 views (x14) | 3.29 | 7.25 | 8.85 |”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The computation time for the FBPConvNet was about 200 ms for the FBP and 200 ∼ 300 ms in GPU for the CNN for a 512 × 512 image.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, in the case of CT reconstruction, if the sinogram is used as input, the CNN must encode a change between polar and Cartesian coordinates, which is completely avoided when the FBP is used as input.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We use high-view FBP reconstructions for training, meaning that training is possible from real data (without oracle knowledge).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
None of the sources cited for this claim have been checked yet.
In the paper
“We clip the computed gradients to a fixed range to prevent the divergence of the cost function [27], [46].”
What the sources say
- Not checked yetcites [27] [27] J. Kim, J. K. Lee, and K. M. Lee, 'Accurate image super-resolution using very deep convolutional networks,' in Proc. of IEEE Converence on Computer Vision and Pattern Recognition (CVPR) , 2016. - source
- Not checked yetcites [46] [46] R. Pascanu, T. Mikolov, and Y. Bengio, 'On the difficulty of training recurrent neural networks.' ICML (3) , vol. 28, pp. 1310-1318, 2013. - source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“We use flip-flop data augmentation in both horizontal and vertical directions during the training phase to reduce overfitting [18].”
What the sources say
- Not checked yetcites [18] [18] A. Krizhevsky, I. Sutskever, and G. E. Hinton, 'Imagenet classification with deep convolutional neural networks,' in Advances in neural information processing systems , 2012, pp. 1097-1105. -
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Many other iterate methods for solving Eq. (5), including ADMM [40], FISTA [41], and SALSA [42], also rely on these basic building blocks.”
What the sources say
- Not matchedcites [40] [40] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, 'Distributed optimization and statistical learning via the alternating direction method of multipliers,' Found. Trends in Mach. Learn. , vol. 3, no. 1, pp. 1-122, 2011. -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites [41] [41] A. Beck and M. Teboulle, 'A fast iterative shrinkage-thresholding algorithm for linear inverse problems,' SIAM journal on imaging sciences , vol. 2, no. 1, pp. 183-202, 2009. - source
- Not checked yetcites [42] [42] M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, 'Fast image recovery using variable splitting and constrained optimization,' IEEE Transactions on Image Processing , vol. 19, no. 9, pp. 2345-2356, 2010. - source
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“In the case of the biomedical dataset, the test data is chosen from a different subject than the training set.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“we instead simply select the parameters that optimize performance on the training set (via a golden-section search).”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The class trivially includes denoising and deconvolution, but also includes MRI [35], X-ray CT [13], [16], and diffraction tomography (DT).”
What the sources say
- Not matchedcites [35] [35] K. P. Pruessmann, M. Weiger, M. B. Scheidegger, P. Boesiger et al. , 'SENSE: sensitivity encoding for fast MRI,' Magn. Reson. Med. , vol. 42, no. 5, pp. 952-962, 1999. -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites [13] [13] M. T. McCann, M. Nilchian, M. Stampanoni, and M. Unser, 'Fast 3D reconstruction method for differential phase contrast X-ray CT,' Opt. Express , vol. 24, no. 13, pp. 14 564-14 581, Jun 2016. - source
- Not checked yetcites [16] [16] E. Y. Sidky and X. Pan, 'Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,' Physics in medicine and biology , vol. 53, no. 17, p. 4777, 2008. - source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
None of the sources cited for this claim have been checked yet.
In the paper
“In practice, inverse problems related with imaging are often ill-posed, which prohibits the use of direct inversion because measurement noise causes serve perturbations in the solution.”
What the sources say
- Not checked yetcites [2] [2] A. Chambolle, 'An algorithm for total variation minimization and applications,' J. Math. imaging and vision , vol. 20, no. 1-2, pp. 89-97, 2004. - source
- Not checked yetcites [9] [9] R. Tibshirani, 'Regression shrinkage and selection via the lasso,' Journal of the Royal Statistical Society. Series B (Methodological) , pp. 267-288, 1996. - source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This formulation does not admit a closed form solution, and, therefore, is typically solved iteratively.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is critical for our application because the filters corresponding to H ∗ H (and its inverse) may have noncompact support, e.g. in CT. Thus, a CNN with a small, fixed filter size may not be able to effectively invert H ∗ H .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“The test data are obtained from the last z-slices with the gap of 25 slices left between testing and training data.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This points to one advantage of the proposed method over iterative methods: the iterative methods must explicitly impose regularization, while the FBPConvNet effectively learns a regularizer from the data.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper relies on this without support.
High-view FBP reconstructions can serve as ground truth for training and evaluation.
“We compute its FBP (standard high quality reconstruction) and take this as the ground truth.”
The paper relies on this without support.
A twenty times reduction in the number of views corresponds to a twenty times reduction in the radiation dose received by the patient.
“a twenty times reduction in the number of views corresponds to a twenty times reduction in the radiation dose received by the patient.”
The paper relies on this without support.
The training and test sets for the synthetic datasets are disjoint.
“In case of synthetic data, the total number of training images is 475. The number of test images is 25.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Their study showed that U-net could effectively produce noiseless CT images from the subsampled sinogram.”
From Convolutional neural networks: an overview and application in radiology (2018) · cites this paper as [54]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Experimental 14-fold case is reported as both 51 and 52 views
MinorThe data-preparation text says the 14-fold subsampling yields 52 views, but Table III labels that case as 51 views.
“For the real data, we subsampled by factors of 5 and 14 corresponding to 145 and 52 views.”
“| avg. SNR (dB) | 51 views (x14) | 3.29 | 7.25 | 8.85 |”
Experimental result is described as 20-fold rather than 14-fold downsampling
MinorThe discussion of Fig. 8 calls it a twenty-times downsampling case, whereas the experimental data-preparation text identifies the corresponding 52-view case as 14-fold downsampling.
“These trends also appears in twenty times downsampling case (x20) in Fig. 8.”
“For the real data, we subsampled by factors of 5 and 14 corresponding to 145 and 52 views.”
Citations
Cites
Deep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., & Sun, J. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.90 · Cited by 235,474 · cited 2×
“We demonstrate the approach on low-view CT reconstruction, using filtered back projection (FBP) and a CNN that makes use of residual learning [29], [39] and multilevel learning [20].”
BackgroundMethodImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155 · cited 3×
“image in the horizontal and vertical directions during the training phase to reduce overfitting [16].”
BackgroundU-Net: Convolutional Networks for Biomedical Image Segmentation
Ronneberger, O., Fischer, P., & Brox, T. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24574-4_28 · Cited by 99,404 · cited 7×
“A more recent trend is deep learning [15], which has arisen as a promising framework providing state-of-the-art performance for image classification [16], [17] and segmentation [18]–[20].”
BackgroundMethodInfluentialLeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482 · cited 2×
“Adding regularization (e.g., total variation [2] or l 1 sparsity as in LASSO [9]) overcomes this problem.”
BackgroundImageNet Large Scale Visual Recognition Challenge
Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., et al. (2015) · International Journal of Computer Vision · doi:10.1007/s11263-015-0816-y · Cited by 39,380 · cited 1×
“A more recent trend is deep learning [15], which has arisen as a promising framework providing state-of-the-art performance for image classification [16], [17] and segmentation [18]–[20].”
BackgroundFully convolutional networks for semantic segmentation
Long, J., Shelhamer, E., & Darrell, T. (2015) · 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2015.7298965 · Cited by 38,834
Rich Feature Hierarchies for Accurate Object Detection and Semantic Segmentation
Girshick, R., Donahue, J., Darrell, T., & Malik, J. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.81 · Cited by 32,684 · cited 1×
“A more recent trend is deep learning [15], which has arisen as a promising framework providing state-of-the-art performance for image classification [16], [17] and segmentation [18]–[20].”
BackgroundNonlinear total variation based noise removal algorithms
Rudin, L., Osher, S., & Fatemi, E. (1992) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 17,214 · cited 2×
“compressed sensing [7] and the related regularizers such as total variation [1], [2], [4], [8], robust and practical algorithms”
BackgroundBoyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Flagged first, then by citations
9 of the 83 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- epperson, 2013, Creation of fully sampled mr data repository for compressed sensing of the knee, Proc SMRT Conf
Cited by
Sorted by citations
Convolutional neural networks: an overview and application in radiology
Yamashita, R., Nishio, M., Do, R. K. G., & Togashi, K. (2018) · Insights into Imaging · doi:10.1007/s13244-018-0639-9 · Cited by 4,682
“One previous study [54] radiological image is much larger than a general image because radiologist expertise is required for annotation.”
BackgroundAll-optical machine learning using diffractive deep neural networks
Lin, X., Rivenson, Y., Yardimci, N. T., Veli, M., Luo, Y., Jarrahi, M., & Ozcan, A. (2018) · Science · doi:10.1126/science.aat8084 · Cited by 2,568
Image reconstruction by domain-transform manifold learning
Zhu, B., Liu, J. Z., Cauley, S. F., Rosen, B. R., & Rosen, M. S. (2018) · Nature · doi:10.1038/nature25988 · Cited by 1,694
Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing
Monga, V., Li, Y., & Eldar, Y. C. (2021) · IEEE Signal Processing Magazine · doi:10.1109/msp.2020.3016905 · Cited by 1,589
“By allowing a slight departure from the original iterative algorithms [13], [27] and extending the representation capacity, the performance of the unrolled networks may be significantly boosted.”
BackgroundMethodISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing
Zhang, J., & Ghanem, B. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00196 · Cited by 1,438
“The tremendous success of deep learning for many image processing applications has also led researchers to consider relating iterative optimization methods to neural networks [16, 39, 43, 32].”
BackgroundTransformers in medical imaging: A survey
Shamshad, F., Khan, S., Zamir, S. W., Khan, M. H., Hayat, M., Khan, F. S., & Fu, H. (2023) · Medical Image Analysis · doi:10.1016/j.media.2023.102802 · Cited by 1,523
Phase recovery and holographic image reconstruction using deep learning in neural networks
Rivenson, Y., Zhang, Y., Günaydın, H., Teng, D., & Özcan, A. (2017) · Light Science & Applications · doi:10.1038/lsa.2017.141 · Cited by 1,097
“Deep learning has recently been applied to solving inverse problems in imaging science such as in super-resolution 43,44 , acceleration of the image acquisition speed of computed tomography (CT) 45 , magnetic resonance imaging (MRI) 46 , photoacoustic tomography 47 and holography 48,49 .”
Deep Learning on Image Denoising: An overview
Tian, C., Fei, L., Zheng, W., Xu, Y., Zuo, W., & Lin, C.-W. (2020) · Neural Networks · doi:10.1016/j.neunet.2020.07.025 · Cited by 1,091
“Due to the insufficiency of real noisy images, additive white noisy images (AWNIs) are widely used to train the denoising model [102].”
MoDL: Model-Based Deep Learning Architecture for Inverse Problems
Aggarwal, H. K., Mani, M., & Jacob, M. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2865356 · Cited by 1,210
“Improved results may be possibly obtained by fixing the sampling pattern during training, as pursued by most of the deep learning image recovery strategies [16], [18], [33], [34], [43], albeit with increased sensitivity to acquisition settings.”
BackgroundADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing
Yang, Y., Sun, J. Z., Li, H., & Xu, Z. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2883941 · Cited by 913
“For arbitrary-sizedwhole image reconstruction, some methods [45], [46], [47], [48], [49] have been introduced to use convolutional layers to learn a mapping from preliminary reconstructed results (e.”
BackgroundMethodOn the use of deep learning for computational imaging
Barbastathis, G., Özcan, A., & Situ, G. (2019) · Optica · doi:10.1364/optica.6.000921 · Cited by 896
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems
Willard, J., Jia, X., Xu, S., Steinbach, M. S., & Kumar, V. (2022) · ACM Computing Surveys · doi:10.1145/3514228 · Cited by 1,498
“Multiple works have shown an effective application for this in computed tomography (CT) reconstructions [45, 135].”
BackgroundOn instabilities of deep learning in image reconstruction and the potential costs of AI
Antun, V., Renna, F., Poon, C., Adcock, B., & Hansen, A. C. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1907377117 · Cited by 845
Learned Primal-Dual Reconstruction
Adler, J., & Öktem, O. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2799231 · Cited by 870
“We re-implemented the algorithm from [7] but found that using the training procedure as stated in the paper gave sub-optimal results.”
MethodDeep learning in medical imaging and radiation therapy
Sahiner, B., Pezeshk, A. X., Hadjiiski, L. M., Wang, X., Drukker, K., Cha, K. H., Summers, R. M., & Giger, M. L. (2018) · Medical Physics · doi:10.1002/mp.13264 · Cited by 763
“Jin et al. 242 described a general framework for the utilization of CNNs for inverse problems, applied the framework to reduce streaking artifacts in sparse-view reconstruction on parallel beam CT, and compared their approach to filtered back projection (FBP) and total variation (TV) techniques.”
MethodLensless computational imaging through deep learning
Sinha, A., Lee, J. W., Li, S., & Barbastathis, G. (2017) · Optica · doi:10.1364/optica.4.001117 · Cited by 713
Solving inverse problems using data-driven models
Arridge, S., Maaß, P., Öktem, O., & Schönlieb, C. (2019) · Acta Numerica · doi:10.1017/s0962492919000059 · Cited by 767
FastSurfer - A fast and accurate deep learning based neuroimaging pipeline
Henschel, L., Conjeti, S., Estrada, S., Diers, K., Fischl, B. R., & Reuter, M. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.117012 · Cited by 729
“…(Kamnitsas et al., 2017; Varghese et al., 2017; Rezaei et al., 2017; Roa-Barco et al., 2017; Chen and Konukoglu, 2018), MR image reconstruction (Jin et al., 2017; Mardani et al., 2019; Schlemper et al., 2018; Yang et al., 2018; Dedmari et al., 2018), prediction of brain related diseases and…”
Rivenson, Y., Göröcs, Z. S., Günaydın, H., Zhang, Y., Wang, H., & Özcan, A. (2017) · Optica · doi:10.1364/optica.4.001437 · Cited by 657
Singh, D., Kumar, V., Vaishali, & Kaur, M. (2020) · European Journal of Clinical Microbiology & Infectious Diseases · doi:10.1007/s10096-020-03901-z · Cited by 658
“Rectified linear unit (ReLU) activation function is used to learn complex functional mappings between the inputs and response variables [31, 32] .”
MethodConvolutional Neural Networks for Inverse Problems in Imaging: A Review
McCann, M. T., Jin, K. H., & Unser, M. A. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2739299 · Cited by 794
“[25] [27] [25] ? x y ˜ H T { y } ˜ H − 1 { y } ˜ x Fig.”
BackgroundMethodInfluentialSelf-citationCompressed Sensing MRI Reconstruction Using a Generative Adversarial Network With a Cyclic Loss
Quan, T. M., Nguyen-Duc, T., & Jeong, W. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2820120 · Cited by 615
“[29] used deep learning to model the inverse problems in medical imaging.”
MethodSaeedi, S., Rezayi, S., Keshavarz, H., & Kalhori, S. R. N. (2023) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-023-02114-6 · Cited by 628
“Machine learning approaches, especially deep learning, can also play a vital role in the analysis, segmentation, and classification of cancer images, especially brain tumors [26].”
BackgroundDeep-learning inversion: A next-generation seismic velocity model building method
Yang, F., & Ma, J. (2019) · Geophysics · doi:10.1190/geo2018-0249.1 · Cited by 632
“Many DL algorithms are built with CNNs and provide state-of-the-art performance in challenging inverse problems such as image reconstruction (Schlemper et al., 2017), superresolution (Dong et al., 2016), X-ray-computed tomography (Jin et al., 2017), and compressive sensing (Adler et al., 2017).”
BackgroundMethodUsing Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods
Lucas, A. M., Iliadis, M., Molina, R., & Katsaggelos, A. K. (2018) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2760358 · Cited by 584
“, image denoising [30], image inpainting [31], optical flow [32], and computed tomography reconstruction [33].”
BackgroundMethodFraming U-Net via Deep Convolutional Framelets: Application to Sparse-View CT
Han, Y., & Ye, J. C. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2823768 · Cited by 590
“Thus, the U-net architecture is good for the sparse view CT reconstruction to deal with the globally distributed streaking artifacts [16], [17].”
BackgroundMethodInfluentialDeep Learning Techniques for Inverse Problems in Imaging
Ongie, G., Jalal, A., Metzler, C. A., Baraniuk, R. G., Dimakis, A. G., & Willett, R. M. (2020) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2020.2991563 · Cited by 647
“1: Denoising auto-encoders [16], U-Net [78], Deep convolutional framelets [79] Unrolled optimization [80–83], Neumann networks [84] amounts to training from (x,y) pairs amounts to training from (x,y) pairs §4.”
BackgroundDeep Generative Adversarial Neural Networks for Compressive Sensing MRI
Mardani, M., Gong, E., Cheng, J. Y., Vasanawala, S. S., Zaharchuk, G., Xing, L., & Pauly, J. M. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2858752 · Cited by 553
“Similarly, [12] uses a deep U-net to learn priors for converting sparse-view CT images to the full-view images.”
BackgroundMethodLian, C., Liu, M., Zhang, J., & Shen, D. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2889096 · Cited by 544
“Inrecent years, deep convolutional neural networks (CNNs) are showing increasingly successful applications in various medical image computing tasks [24], [25], [26], [27], [28], [29], [30].”
BackgroundDeep learning for tomographic image reconstruction
Wang, G., Ye, J. C., & De Man, B. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-00273-z · Cited by 531
Fully Dense UNet for 2-D Sparse Photoacoustic Tomography Artifact Removal
Guan, S., Khan, A. A., Sikdar, S., & Chitnis, P. V. (2020) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2019.2912935 · Cited by 538
Solving ill-posed inverse problems using iterative deep neural networks
Adler, J., & Öktem, O. (2017) · Inverse Problems · doi:10.1088/1361-6420/aa9581 · Cited by 688
“An example demonstrating this approach for tomographic reconstruction is given in [20, 22].”
MethodYuan, Q., Zhang, Q., Li, J., Shen, H., & Zhang, L. (2018) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2018.2865197 · Cited by 540
Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction
Belthangady, C., & Royer, L. A. (2019) · Nature Methods · doi:10.1038/s41592-019-0458-z · Cited by 515
Convolutional Neural Network Based Metal Artifact Reduction in X-Ray Computed Tomography
Zhang, Y., & Yu, H. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2823083 · Cited by 499
Deep learning in nano-photonics: inverse design and beyond
Wiecha, P. R., Arbouet, A., Girard, C., & Muskens, O. L. (2021) · Photonics Research · doi:10.1364/prj.415960 · Cited by 549
Deep-Learning Schemes for Full-Wave Nonlinear Inverse Scattering Problems
Wei, Z., & Chen, X. (2018) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2018.2869221 · Cited by 500
“This approach is particular well suited to BPS and DCS proposed in the manuscript since the inputs and outputs share similar important features, and it also mitigates the vanishing gradient problem during training [24], [31].”
BackgroundMethodInfluentialRadioUNet: Fast Radio Map Estimation With Convolutional Neural Networks
Levie, R., Yapar, Ç., Gitta Kutyniok, B., & Caire, G. (2021) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2021.3054977 · Cited by 544
“2) UNets: UNet is a special CNN architecture, introduced in [37], and used in a multitude of applications, including image segmentation [41]–[44], video predicting [45], super resolution/image inpainting [46], inverse problems in imaging [47], image-to-image translation [48], and medical image analysis [49] to name a…”
MethodEo, T., Jun, Y., Kim, T., Jang, J., Lee, H., & Hwang, D. (2018) · Magnetic Resonance in Medicine · doi:10.1002/mrm.27201 · Cited by 455
“Meanwhile, several recent studies have demonstrated the applicability of deep-learning techniques to the reconstruction of undersampled MR images(19-21) or CT images.(22) In training, tuples of undersampled images and fully sampled images are fed to convolutional neural networks (CNNs) to learn the relationship betwee…”
BackgroundMethodInfluentialDeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering
Li, L., Wang, L. G., Teixeira, F. L., Liu, C., Nehorai, A., & Cui, T. J. (2018) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2018.2885437 · Cited by 459
A Sparse-View CT Reconstruction Method Based on Combination of DenseNet and Deconvolution
Zhang, Z., Liang, X., Xu, D., Xie, Y., & Cao, G. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2823338 · Cited by 465
“Jin et al. [35] proposed a deep convolutional network (FBPConvNet) that combines FBP and U-net, and made full use of multi-resolution CNN [36] and residual learning [37].”
BackgroundMethodLEARN: Learned Experts’ Assessment-Based Reconstruction Network for Sparse-Data CT
Chen, H., Zhang, Y., Chen, Y., Zhang, J., Zhang, W., Sun, H., Lv, Y., Liao, P., Zhou, J., & Wang, G. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2805692 · Cited by 464
Seo, H., Huang, C. W., Bassenne, M., Xiao, R., & Xing, L. (2019) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2019.2948320 · Cited by 441
“Recently, inspired by the tremendous success of deep learning in classification [9], [10],”
BackgroundImaging through glass diffusers using densely connected convolutional networks
Li, S., Deng, M., Lee, J. W., Sinha, A., & Barbastathis, G. (2018) · Optica · doi:10.1364/optica.5.000803 · Cited by 441
One-step robust deep learning phase unwrapping
Wang, K., Li, Y., Kemao, Q., Di, J., & Zhao, J. (2019) · Optics Express · doi:10.1364/oe.27.015100 · Cited by 421
Shan, H., Zhang, Y., Yang, Q., Krüger, U., Kalra, M. K., Sun, L., Cong, W., & Wang, G. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2832217 · Cited by 467
“There are several existing designs close to the CPCE denoising network [6], [32]–[34].”
CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction
Gupta, H., Jin, K. H., Nguyen, H. Q., McCann, M. T., & Unser, M. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2832656 · Cited by 436
“3) Learning-Based Algorithms: Recently, a surge in using deep learning to solve inverse problems in imaging [15]–[19], has established new state-of-the-art results for tasks such as sparse-view CT reconstruction [16].”
BackgroundMethodInfluentialSelf-citationDeep-Learning Inversion of Seismic Data
Li, S., Liu, B., Ren, Y., Chen, Y., Yang, S., Wang, Y., & Jiang, P. (2019) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2019.2953473 · Cited by 423
“For example, medical image semantic segmentation methods such as U-Net [23], [37] concatenate low-level features on the output of deep layers by shortcuts to compensate details of the results, but they only work on data where input and output are spatially aligned.”
BackgroundMethodIntelligent metasurface imager and recognizer
Li, L., Shuang, Y., Ma, Q., Li, H., Zhao, H., Wei, M., Liu, C., Hao, C., Qiu, C., & Cui, T. J. (2019) · Light Science & Applications · doi:10.1038/s41377-019-0209-z · Cited by 386
Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks
Hamilton, S. J., & Hauptmann, A. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2828303 · Cited by 369
“This successful transition to experimental data underlines the robustness of the D-bar algorithm and is especially important as the need for good training data is often the bottleneck for the success of such network-based approaches for other imaging modalities, [14], [18], [19].”
BackgroundMethodResultInfluentialJeyaraj, P. R., & Nadar, E. R. S. (2019) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-018-02834-7 · Cited by 366
Deep Residual Learning for Accelerated MRI Using Magnitude and Phase Networks
Lee, D., Yoo, J., Tak, S., & Ye, J. C. (2018) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2018.2821699 · Cited by 340
“However, U-net has limitations due to duplication of low frequency content [32].”
BackgroundInfluentialModel-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography
Hauptmann, A., Lucka, F. F., Betcke, M. M., et al. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2820382 · Cited by 346
“For our application, we have followed the modified U-Net architecture proposed by [20] for post-processing of 2D X-ray tomography, that learns to compute an update to the initial reconstruction.”
BackgroundMethodIntelligent metasurfaces: control, communication and computing
Li, L., Zhao, H., Li, L., Li, L., & Cui, T. J. (2022) · eLight · doi:10.1186/s43593-022-00013-3 · Cited by 359
PointCleanNet : Learning to Denoise and Remove Outliers from Dense Point Clouds
Rakotosaona, M., Barbera, V. L., Guerrero, P., Mitra, N. J., & Ovsjanikov, M. (2019) · Computer Graphics Forum · doi:10.1111/cgf.13753 · Cited by 381
Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems
Ye, J. C., Han, Y., & Cha, E. (2018) · SIAM Journal on Imaging Sciences · doi:10.1137/17m1141771 · Cited by 332
“For example, in image denoising [40, 76] or streaking artifact problems [28, 35], a residual network works better, since the artifacts are random and have complicated distribution.”
BackgroundMethodInfluential${k}$ -Space Deep Learning for Accelerated MRI
Han, Y., Sunwoo, L., & Ye, J. C. (2019) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2019.2927101 · Cited by 354
Metasurface-enabled on-chip multiplexed diffractive neural networks in the visible
Luo, X., Hu, Y., Ou, X., Li, X., Lai, J., Liu, N., Cheng, X., Pan, A., & Duan, H. (2022) · Light: Science & Applications · doi:10.1038/s41377-022-00844-2 · Cited by 335
One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models
Chang, J.-Y., Li, C., Póczos, B., Kumar, B. V. K. V., & Sankaranarayanan, A. C. (2017) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.627 · Cited by 347
“Many recent works solve linear inverse problems by unrolling the optimization process into the network architecture [3,6,22,26].”
BackgroundHäggström, I., Schmidtlein, C. R., Campanella, G. S. V., & Fuchs, T. J. (2019) · Medical Image Analysis · doi:10.1016/j.media.2019.03.013 · Cited by 322
HSI-DeNet: Hyperspectral Image Restoration via Convolutional Neural Network
Chang, Y., Yan, L., Fang, H., Zhong, S., & Liao, W. (2018) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2018.2859203 · Cited by 319
“Many works [20], [54] have discussed their relationship and design their deep architecture based on the optimization solvers.”
BackgroundMethodFISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging
Xiang, J., Dong, Y., & Yang, Y. (2021) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2021.3054167 · Cited by 329
“FBPConvNet is a network-based method.”
BackgroundInfluentialDeep learning with domain adaptation for accelerated projection‐reconstruction MR
Han, Y., Yoo, J., Kim, H. H., Shin, H. J., Sung, K., & Ye, J. C. (2018) · Magnetic Resonance in Medicine · doi:10.1002/mrm.27106 · Cited by 292
“25 Jin et al. 26 and Han et al. 27 independently proposed multi-scale residual learning networks using U-Net 15 to remove the global streaking artifacts caused by sparse projection views.”
MethodImage Reconstruction: From Sparsity to Data-Adaptive Methods and Machine Learning
Ravishankar, S., Ye, J. C., & Fessler, J. A. (2019) · Proceedings of the IEEE · doi:10.1109/jproc.2019.2936204 · Cited by 345
“FBPConvNet [141] extended the LISTA interpretation for one specific class of inverse problems: those where the normal operator associated with the forward model ( W = I − 1 A (cid:62) A ) is a convolution.”
BackgroundMethodInfluentialIntegrating Physics-Based Modeling with Machine Learning: A Survey
Willard, J., Jia, X., Xu, S., Steinbach, M. S., & Kumar, V. (2020) · Cited by 299
A Review of the Deep Learning Methods for Medical Images Super Resolution Problems
Li, Y., Sixou, B., & Peyrin, F. (2020) · IRBM · doi:10.1016/j.irbm.2020.08.004 · Cited by 295
“In particular, DL for medical imaging has achieved amazing progresses in fields such as image reconstruction[5], denoising[6], super resolution[4], segmentation [7], computed-assistant diag20”
MethodA review on medical imaging synthesis using deep learning and its clinical applications
Wang, T., Lei, Y., Fu, Y., Wynne, J. F., Curran, W. J., Liu, T., & Yang, X. (2020) · Journal of Applied Clinical Medical Physics · doi:10.1002/acm2.13121 · Cited by 305
“120 Among image domain methods, Shan et al. used a progressive scheme that iteratively denoised the input LDCT, yielding a sequence of denoised images at different noise levels.”
MethodQuantitative phase imaging based on holography: trends and new perspectives
Huang, Z., & Cao, L. (2024) · Light Science & Applications · doi:10.1038/s41377-024-01453-x · Cited by 310
“When it is used to solve real-world physical problems, DNN has met with limited success due to several reasons: First, DNN requires a large amount of labeled data for training, which is not always available in real application settings 353 .”
MethodInfluentialImage Reconstruction Based on Convolutional Neural Network for Electrical Resistance Tomography
Tan, C., Lv, S., Dong, F., & Takei, M. (2018) · IEEE Sensors Journal · doi:10.1109/jsen.2018.2876411 · Cited by 265
“using ad hoc architecture design [29] or unrolling an iterative optimization algorithm [30].”
MethodKnöll, F., Murrell, T., Sriram, A., Yakubova, N., Žbontar, J., Rabbat, M., Defazio, A., Muckley, M. J., Sodickson, D. K., Zitnick, C. L., et al. (2020) · Magnetic Resonance in Medicine · doi:10.1002/mrm.28338 · Cited by 274
“Machine learning has been proposed for CT dose reduction [1, 2, 3, 4, 5, 6], attenuation correction for PET-MRI [7] and acceleratedMR imaging [8, 9, 10, 11, 12, 13, 14, 15, 16].”
MethodPlug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery
Ahmad, R., Bouman, C. A., Buzzard, G. T., Chan, S. H., Liu, S., Reehorst, E. T., & Schniter, P. (2020) · IEEE Signal Processing Magazine · doi:10.1109/msp.2019.2949470 · Cited by 256
Ding, Y., Wu, G., Chen, D., Zhang, N., Gong, L., Cao, M., & Qin, Z. (2020) · IEEE Internet of Things Journal · doi:10.1109/jiot.2020.3012452 · Cited by 301
Deep learning approach for Fourier ptychography microscopy
Nguyen, T., Xue, Y., Li, Y., Tian, L., & Nehmetallah, G. (2018) · Optics Express · doi:10.1364/oe.26.026470 · Cited by 293
Shallow neural networks for fluid flow reconstruction with limited sensors
Erichson, N. B., Mathelin, L., Yao, Z., Brunton, S. L., Mahoney, M. W., & Kutz, J. N. (2020) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2020.0097 · Cited by 296
“In particular, deep inverse transform learning is an emerging concept [14, 15, 16, 17], which has been shown to outperform traditional methods in applications such as denoising, deconvolution, and super-resolution.”
MethodDeep-Neural-Network-Based Sinogram Synthesis for Sparse-View CT Image Reconstruction
Lee, H., Lee, J., Kim, H., Cho, B., & Cho, S. (2018) · IEEE Transactions on Radiation and Plasma Medical Sciences · doi:10.1109/trpms.2018.2867611 · Cited by 304
“Adding the residual learning scheme to the U-Net showed enhanced performances in removing streak artifacts in medical imaging [35], [36].”
MethodFaroughi, S. A., Pawar, N. M., Fernandes, C. B. P., Raissi, M., Das, S., Kalantari, N. K., & Mahjour, S. K. (2024) · Journal of Computing and Information Science in Engineering · doi:10.1115/1.4064449 · Cited by 430
DuDoNet: Dual Domain Network for CT Metal Artifact Reduction
Lin, W.-A., Liao, H., Peng, C., Sun, X., Zhang, J., Luo, J., Chellappa, R., & Zhou, S. K. (2019) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2019.01076 · Cited by 281
“Methods in [26, 10, 1, 34] target image formation via deep learning, which is not the main focus of this work.”
BackgroundIterative Low-Dose CT Reconstruction With Priors Trained by Artificial Neural Network
Wu, D., Kim, K., Fakhri, G. E., & Li, Q. (2017) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2017.2753138 · Cited by 256
Hauptmann, A., Arridge, S., Lucka, F. F., Muthurangu, V., & Steeden, J. A. (2018) · Magnetic Resonance in Medicine · doi:10.1002/mrm.27480 · Cited by 243
“nstruction compared to a current state-of-the-art CS algorithm. METHODS Deep De-aliasing Algorithm – General concept The deep de-aliasing algorithm was based on a modified residual U-Net architecture (11,12). A residual U-Net is a multi-scale CNN where images are sequentially down-sampled and then up-sampled to produc…”
MethodPhysics-Inspired Convolutional Neural Network for Solving Full-Wave Inverse Scattering Problems
Wei, Z., & Chen, X. (2019) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2019.2922779 · Cited by 249
“A parametric reconstruction algorithm Rl is learned by solving [38] Rl = argmin Rθ ,θ : Mt∑ m=1 f ( Rθ ( E s m ) , ξm ) + g(θ) (9) where Rθ represents an ANN with specific architecture and parameters θ are the weights to be learned in Rθ .”
InfluentialNETT: solving inverse problems with deep neural networks
Li, H., Schwab, J., Antholzer, S., & Haltmeier, M. (2020) · Inverse Problems · doi:10.1088/1361-6420/ab6d57 · Cited by 260
“Very recently, several deep learning approaches for inverse problems have been developed.[1, 3, 8, 23, 24, 39, 21, 36, 40, 41].”
BackgroundDRONE: Dual-Domain Residual-based Optimization NEtwork for Sparse-View CT Reconstruction
Wu, W., Hu, D., Niu, C., Yu, H., Vardhanabhuti, V., & Wang, G. (2021) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2021.3078067 · Cited by 243
On the use of deep learning for phase recovery
Wang, K., Song, L., Wang, C., Ren, Z., Zhao, G., Dou, J., Di, J., Barbastathis, G., Zhou, R., Zhao, J., et al. (2023) · Light Science & Applications · doi:10.1038/s41377-023-01340-x · Cited by 257
“Similarly, since it was fi rst used to solve the inverse problem in imaging in 2016 58 , deep learning has demonstrated promising potential in the fi eld of computational imaging 59 .”
MethodMachine learning integrated design for additive manufacturing
Jiang, J., Xiong, Y., Zhang, Z., & Rosen, D. W. (2020) · Journal of Intelligent Manufacturing · doi:10.1007/s10845-020-01715-6 · Cited by 234
Cycle‐consistent adversarial denoising network for multiphase coronary CT angiography
Kang, E., Koo, H. J., Yang, D. H., Seo, J. B., & Ye, J. C. (2018) · Medical Physics · doi:10.1002/mp.13284 · Cited by 230
Nonlocal Patch Tensor Sparse Representation for Hyperspectral Image Super-Resolution
Xu, Y., Wu, Z., Chanussot, J., & Wei, Z. (2019) · IEEE Transactions on Image Processing · doi:10.1109/tip.2019.2893530 · Cited by 233
“With the successful application of deep learning in object detection [17]–[19], classification [20]–[22], low-level inverse problems [23]–[25], many researchers have applied deep learning to HSI super-resolution.”
BackgroundInversionNet: An Efficient and Accurate Data-Driven Full Waveform Inversion
Wu, Y., & Lin, Y. (2019) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2019.2956866 · Cited by 257
“solving inverse problems in many scientific domains [18], [35].”
BackgroundApplication of neural network algorithm in fault diagnosis of mechanical intelligence
Xu, X., Cao, D. T. N., Zhou, Y., & Gao, J. Y. (2020) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2020.106625 · Cited by 233
lambda-Net: Reconstruct Hyperspectral Images From a Snapshot Measurement
Miao, X., Yuan, X., Pu, Y., & Athitsos, V. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00416 · Cited by 230
“To address this and inspired by the recent advances of deep learning on image restoration [71, 88], researchers have started using deep learning in computational imaging [13, 28, 32, 36, 46, 42, 54, 72, 82, 78].”
BackgroundLearning-based lensless imaging through optically thick scattering media
Lyu, M., Wang, H., Li, G., Zheng, S., & Situ, G. (2019) · Advanced Photonics · doi:10.1117/1.ap.1.3.036002 · Cited by 223
eHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction
Wang, H., Lyu, M., & Situ, G. (2018) · Optics Express · doi:10.1364/oe.26.022603 · Cited by 223
Deep Learning Inversion of Electrical Resistivity Data
Liu, B., Guo, Q., Li, S., Liu, B., Ren, Y., Pang, Y., Guo, X., Liu, L., & Jiang, P. (2020) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2020.2969040 · Cited by 237
“Many attempts have already verified that DNNs could approximate very complex nonlinear mapping functions, especially for ill-posed inverse problems, such as image superresolution [31], medical imaging [32], and 3-D model reconstruction [33].”
BackgroundXu, G., Zhang, B., Yu, H., Chen, J., Xing, M., & Hong, W. (2022) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2022.3218801 · Cited by 232
“OTHER ARCHITECTURES OF NEURAL NETWORKS Next, two neural networks that are also related to sparse reconstruction, RNN [63] and GAN [149], are introduced.”
BackgroundMethodInfluentialEnhanced Radar Imaging Using a Complex-Valued Convolutional Neural Network
Gao, J., Deng, B., Qin, Y., Wang, H., & Li, X. (2018) · IEEE Geoscience and Remote Sensing Letters · doi:10.1109/lgrs.2018.2866567 · Cited by 212
“[12] pointed out the similarity between the iterative shrinkage methods and the feedforward process of CNN.”
MethodWe, Z., & Li, X. (2021) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2021.3065522 · Cited by 210
Improvement of image quality at CT and MRI using deep learning
Higaki, T., Nakamura, Y., Tatsugami, F., Nakaura, T., & Awai, K. (2018) · Japanese Journal of Radiology · doi:10.1007/s11604-018-0796-2 · Cited by 214
Review of Vibration-Based Structural Health Monitoring Using Deep Learning
Toh, G., & Park, J. (2020) · Applied Sciences · doi:10.3390/app10051680 · Cited by 225
Time-Dependent Deep Image Prior for Dynamic MRI
Yoo, J., Jin, K. H., Gupta, H., Yerly, J., Stuber, M., & Unser, M. A. (2021) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2021.3084288 · Cited by 200
Self-citationPlug-and-Play Algorithms for Large-Scale Snapshot Compressive Imaging
Yuan, X., Liu, Y., Suo, J., & Dai, Q. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.00152 · Cited by 222
“Inspired by deep learning on image restoration [74], researchers have started using deep learning in computational imaging [16, 19, 20, 30, 39, 29, 65].”
BackgroundQuantitative susceptibility mapping using deep neural network: QSMnet
Yoon, J., Gong, E., Chatnuntawech, I., Bilgic, B., Lee, J., Jung, W., Ko, J., Jung, H., Setsompop, K., Zaharchuk, G., et al. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2018.06.030 · Cited by 185
“…was originally proposed for biomedical image segmentation (Ronneberger et al., 2015) and have showed great performance for image reconstruction (Gong et al., 2017; Han et al., 2016; Isola et al., 2017; Jin et al., 2017; Lee et al., 2017a; Yu et al., 2017), was used as a base structure of QSMnet.”
Method
Metadata
- Authors
- Jin, K. H., McCann, M. T., Froustey, E., & Unser, M.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- Dassault Aviation (France) (FR)
- Venue
- IEEE Transactions on Image Processing
- Published
- 2017-09
- Volume
- 26
- Issue
- 9
- Pages
- 4509-4522
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2574952845
- Semantic Scholar
- 8a68ca7c5ba4d92de3435961f88188d0b769b920
- Cited by
- 2,529
- References
- 83
- Citations by year
- 2026: 184 · 2025: 280 · 2024: 291 · 2023: 318 · 2022: 317 · 2021: 383 · 2020: 326 · 2019: 277 · 2018: 128 · 2017: 23
- FWCI
- 228.23
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Image Processing (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DORA PSI (Paul Scherrer Institute) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- H2020 European Research Council (the European Research Council under Grant 692726 ()
- Centre dImagerie BioMedicale
- EPFL Fellows fellowship program co-funded by Marie Curie from the EuropeanUnions Horizon 2020 Framework Programme for Research and Innovation (665667)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Keywords
- deep convolutional neural networks, ill-posed inverse problems, direct inversion, artifact removal, multiresolution decomposition, residual learning, sparse-view reconstruction, total variation regularization, image reconstruction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
