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.
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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.
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Claims the paper makes
0 of 13 cited sources checked · 0 supported · 0 flagged
- Findingnone given§ Abstract · p. 1
The proposed network requires less than a second to reconstruct a 512 × 512 image on the GPU.
“requires less than a second to reconstruct a 512 × 512 image on the GPU.”
Quote in the paperSubstantial claim- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
- Findingown data§ B. Biomedical Dataset · p. 13
For the biomedical dataset, the sparse-view FBP contains line artifacts.
“In Figure 5, again, the sparse-view FBP contains line artifacts.”
Quote in the paperNot a substantial claim - Findingown data§ A. Ellipsoidal Dataset · p. 11
For the ellipsoidal dataset at 143 views, both the TV and FBPConvNet methods significantly reduce these artifacts, giving visually indistinguishable results.
“Both the TV and FBPConvNet methods significantly reduce these artifacts, giving visually indistinguishable results.”
Quote in the paperNot a substantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
- Findingnone given§ Skip connection · p. 9
Adding a skip connection between input and output (residual learning) yields a noticeable increase in performance compared to the same network without the skip connection.
“This yields a noticeable increase in performance compared to the same network without the skip connection.”
Quote in the paperNot a substantial claim- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
- Findingown data§ Abstract · p. 1
The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms.
“The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms”
Quote in the paperSubstantial claim- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
- Findingreasoning§ A. Ellipsoidal Dataset · p. 11
For the ellipsoidal dataset, the average SNR on the testing set for the TV method is higher than that of the FBPConvNet.
“The average SNR on the testing set for the TV method is higher than that of the the FBPConvNet.”
Quote in the paperNot a substantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
- Findingown data§ Abstract · p. 1
The proposed network was demonstrated in sparse-view reconstruction down to 50 views on parallel beam X-ray computed tomography in synthetic phantoms and real experimental sinograms.
“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.”
Quote in the paperSubstantial claim- 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.
- Findingnone given§ I. INTRODUCTION · p. 3
Reconstructed images from the proposed network represented well complex textures which are important to diagnosis.
“Especially, reconstructed images from the proposed network represented well complex textures which are important to diagnosis.”
Quote in the paperNot a substantial claim- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
- Findingreasoning§ A. Theory · p. 4
A version of Theorem 1 also holds in the discrete case.
“A version of Theorem 1 also holds in the discrete case; we sketch the result here.”
Quote in the paperNot a substantial claim - Findingown data§ A. Ellipsoidal Dataset · p. 11
For the ellipsoidal dataset at 20x downsampling, the line artifacts in the sparse-view FBP reconstruction are even more pronounced.
“When the downsampling is increased to twenty times, Figure 4, the line artifacts in the sparse-view FBP reconstruction are even more pronounced.”
Quote in the paperNot a substantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
- Findingreasoning§ A. Theory · p. 4
If there exists an isometry T, a multiplication M_m, and a change of variables Φ_φ such that H = T M_m Φ^{-1}_φ F, then H*H is a convolution with h-hat = |det J_φ| M_{Φ_φ |m|^2}.
“If there exists an isometry, T , a multiplication, M m , and a change of variables, Φ ϕ , such that H = TM m Φ -1 ϕ F , then H ∗ H is a convolution with ˆ h = | det J ϕ | M Φ ϕ | m | 2 , where J ϕ is the Jacobian matrix of ϕ and M Φ ϕ | m | 2 is a suitable multiplication.”
Quote in the paperSubstantial claim - Findingreasoning§ A. Theory · p. 4
For the continuous 2D X-ray transform R, R*R is a convolution with h-hat(ω) = 1/||ω||.
“Theorem 1 states that R ∗ R is a convolution with ˆ h ( ω ) = | det J ϕ ( ω ) | = 1 / ‖ ω ‖ , where, again, ω is the frequency variable associated with the 2D Fourier transform, F .”
Quote in the paperSubstantial claim - Findingown data§ VI. DISCUSSION · p. 16
A major limitation of the proposed method is lack of transfer between datasets.
“A major limitation of the proposed method is lack of transfer between datasets.”
Quote in the paperNot a substantial claim - Findingown data§ VII. CONCLUSION · p. 17
The proposed method compared favorably to state-of-the-art iterative reconstruction on the two more realistic datasets.
“It compared favorably to state-of-the-art iterative reconstruction on the two more realistic datasets.”
Quote in the paperSubstantial claim - Findingown data§ VII. CONCLUSION · p. 17
The proposed method demonstrated compelling results on synthetic and real data.
“The proposed method demonstrated compelling results on synthetic and real data.”
Quote in the paperSubstantial claim - Findingown data§ B. Biomedical Dataset · p. 13
Quantitatively, the proposed method outperforms the TV method on the biomedical dataset.
“Quantitatively, the proposed method outperforms the TV method.”
Quote in the paperSubstantial claim - Findingnone given§ VII. CONCLUSION · p. 16
We showed conditions on a linear operator that ensure that its normal operator is a convolution.
“Specifically, we showed conditions on a linear operator that ensure that its normal operator is a convolution.”
Quote in the paperSubstantial claim - Findingown data§ C. Experimental Dataset · p. 15
For the experimental dataset, the FBPConvNet had a higher SNR than the TV method in both settings.
“The FBPConvNet had a higher SNR than the TV method in both settings.”
Quote in the paperSubstantial claim - Findingown data§ VI. DISCUSSION · p. 16
When FBP images from a twenty-times subsampled sinogram are put into the network trained on the seven-times subsampled sinogram, the results retain many artifacts.
“For instance, when we put FBP images from a twenty-times subsampled sinogram into the network trained on the seven-times subsampled sinogram, the results retain many artifacts.”
Quote in the paperSubstantial claim - Findingown data§ B. Biomedical Dataset · p. 13
For the biomedical dataset at 20x downsampling, the same trend is observed.
“This trend is also observed in severe case (x20) in Fig. 6.”
Quote in the paperNot a substantial claim - Findingown data§ C. Experimental Dataset · p. 15
For the experimental dataset at 20x downsampling, these trends also appear.
“These trends also appears in twenty times downsampling case (x20) in Fig. 8.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ B. Training Procedure · p. 10
The training strategy of using low-view FBP images as input and full-view FBP images as output means that the method is applicable to real CT reconstructions where we do not have access to an oracle reconstruction.
“Note that this training strategy means that the method is applicable to real CT reconstructions where we do not have access to an oracle reconstruction.”
Quote in the paperSubstantial claim - Premisecitation§ A. Ellipsoidal Dataset · p. 11
TV regularization should be optimal for piecewise constant phantoms.
“This is a reasonable results given that the phantom is piecewise constant and thus the TV regularization should be optimal [2], [47].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [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 in the free run.
- cites [47] [47] M. Unser, J. Fageot, and H. Gupta, 'Representer theorems for sparsity-promoting ℓ 1 regularization,' IEEE Transactions on Information Theory , vol. 62, no. 9, pp. 5167-5180, September 2016. source
Not checked in the free run.
- Premisenone given§ Abstract · p. 1
Unrolled iterative methods have the form of a CNN (filtering followed by point-wise non-linearity) when the normal operator H*H of the forward model is a convolution.
“The starting point of our work is the observation that unrolled iterative methods have the form of a CNN (filtering followed by point-wise non-linearity) when the normal operator ( H ∗ H , the adjoint of H times H ) of the forward model is a convolution.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ A. Filtered Back Projection · p. 7
Efficient, direct inversions are always available for normal-convolutional inverse problems.
“We stress again that, while the FBP is specific to CT, Section II-C shows that efficient, direct inversions are always available for normal-convolutional inverse problems.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ III. PROPOSED METHOD: FBPCONVNET · p. 6
The FBPConvNet approach applies in principle to all normal-convolutional inverse problems.
“This approach applies in principle to all normal-convolutional inverse problems, but we have focused in this work on CT reconstruction.”
Quote in the paperSubstantial claim - Interpretationreasoning§ II. INVERSE PROBLEMS WITH SHIFT-INVARIANT NORMAL OPERATORS · p. 3
Solving normal-convolutional inverse problems iteratively requires repeated convolutions and point-wise nonlinearities.
“As we will show, solving problems of this form iteratively requires repeated convolutions and point-wise nonlinearities, which suggests that CNNs may offer an alternative solution.”
Quote in the paperSubstantial claim - Interpretationreasoning§ A. Filtered Back Projection · p. 7
Performing FBP first greatly simplifies the learning compared to training a CNN to regress directly from the measurement domain to the reconstruction domain.
“While it would be possible to train a CNN to regress directly from the measurement domain to the reconstruction domain, performing the FBP first greatly simplifies the learning.”
Quote in the paperSubstantial claim - Interpretationown data§ VI. DISCUSSION · p. 16
The experiments provide strong evidence for the feasibility of the FBPConvNet for sparse-view CT reconstruction.
“The experiments provide strong evidence for the feasibility of the FBPConvNet for sparse-view CT reconstruction.”
Quote in the paperSubstantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
- Interpretationnone given§ VI. DISCUSSION · p. 16
The methodology proposed here is applicable to all problems where the normal operator is shift-invariant.
“Our theory suggests that the methodology proposed here is applicable to all problems where the normal operator is shift-invariant”
Quote in the paperNot a substantial claim - Interpretationnone given§ VI. DISCUSSION · p. 16
In the more-realistic datasets, the SNR improvement of the FBPConvNet came from its ability to preserve fine details in the images.
“In these more-realistic datasets, the SNR improvement of the FBPConvNet came from its ability to preserve fine details in the images.”
Quote in the paperSubstantial claim - Interpretationreasoning§ VII. CONCLUSION · p. 16
CNNs are well-suited to the subclass of inverse problems where the normal operator is a convolution.
“This results suggests that CNNs are well-suited to this subclass of inverse problems.”
Quote in the paperSubstantial claim - Interpretationown data§ C. Experimental Dataset · p. 15
For the experimental dataset, the SNRs of all methods are significantly lower because of the relatively low contrast of the sinogram.
“The SNRs of all methods are significantly lower here because of the relatively low contrast of the sinogram.”
Quote in the paperNot a substantial claim - Interpretationown data§ VI. DISCUSSION · p. 16
Handling datasets of different dimensions or subsampling factors requires retraining the network.
“Handling datasets of different dimensions or subsampling factors requires retraining the network.”
Quote in the paperSubstantial claim
- May combine two claims. 20
- Classified as probably not a substantial claim. 8
May combine two claims.
Findingown data§ A. Ellipsoidal Dataset · p. 12For the ellipsoidal dataset at 50 views, the average SNR was 8.44 dB for FBP, 27.69 dB for TV, and 23.84 dB for FBPConvNet.
“| avg. SNR (dB) | 50 views (x20) | 8.44 | 27.69 | 23.84 |”
Quote in the paperSubstantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
May combine two claims.
Findingown data§ A. Ellipsoidal Dataset · p. 11For the ellipsoidal dataset at 143 views, the full-view FBP shows nearly artifact-free ellipsoids, while the sparse-view FBP shows significant line artifacts.
“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).”
Quote in the paperSubstantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
May combine two claims.
Findingown data§ A. Ellipsoidal Dataset · p. 12For the ellipsoidal dataset at 143 views, the average SNR was 16.09 dB for FBP, 29.48 dB for TV, and 28.96 dB for FBPConvNet.
“| avg. SNR (dB) | 143 views (x7) | 16.09 | 29.48 | 28.96 |”
Quote in the paperSubstantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
May combine two claims.
Findingown data§ A. Ellipsoidal Dataset · p. 11For the ellipsoidal dataset at 20x downsampling, both the TV and FBPConvNet reduce these artifacts, though the FBPConvNet retains some of the artifacts.
“Both the TV and FBPConvNet reduce these artifacts, though the FBPConvNet retains some of the artifacts.”
Quote in the paperNot a substantial claim- Rests on an assumption: The training and test sets for the synthetic datasets are disjoint.
Classified as probably not a substantial claim.
Findingreasoning§ C. Iterative Inversion · p. 6When the forward model is normal-convolutional and W is a convolution, ISTA 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.
“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 .”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ B. Biomedical Dataset · p. 13For the biomedical dataset at 50 views, the average SNR was 13.52 dB for FBP, 25.2 dB for TV, and 28.83 dB for FBPConvNet.
“| avg. SNR (dB) | 50 views (x20) | 13.52 | 25.2 | 28.83 |”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ C. Experimental Dataset · p. 15For the experimental dataset, the same trend as for the biomedical dataset is observed, where the TV method oversmooths and the FBPConvNet better preserves fine structures.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ VI. DISCUSSION · p. 16The FBPConvNet computation time is much faster than the iterative reconstruction, which requires around 7 minutes even after the regularization parameters have been selected.
“This is much faster than the iterative reconstruction, which, in our case, requires around 7 minutes even after the regularization parameters have been selected.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Findingnone given§ VII. CONCLUSION · p. 17After training, the computation time of the proposed network per one image is under a second.
“Furthermore, after training, the computation time of the proposed network per one image is under a second.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ VI. DISCUSSION · p. 16The conventional iterative algorithm with TV regularization outperformed the FBPConvNet in the ellipsoidal dataset, while the reverse was true for the biomedical and experimental datasets.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ B. Biomedical Dataset · p. 15For the experimental dataset at 145 views, the average SNR was 5.38 dB for FBP, 8.25 dB for TV, and 11.34 dB for FBPConvNet.
“| avg. SNR (dB) | 145 views (x5) | 5.38 | 8.25 | 11.34 |”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ B. Biomedical Dataset · p. 13For the biomedical dataset at 143 views, the average SNR was 24.97 dB for FBP, 31.92 dB for TV, and 36.15 dB for FBPConvNet.
“| avg. SNR (dB) | 143 views (x7) 24.97 | | 31.92 36.15 | |”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ B. Biomedical Dataset · p. 13For the biomedical dataset, both TV and the proposed method remove streaking artifacts satisfactorily; however, the TV reconstruction shows cartoon-like artifacts typical of TV reconstructions.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ B. Biomedical Dataset · p. 15For the experimental dataset at 51 views, the average SNR was 3.29 dB for FBP, 7.25 dB for TV, and 8.85 dB for FBPConvNet.
“| avg. SNR (dB) | 51 views (x14) | 3.29 | 7.25 | 8.85 |”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ VI. DISCUSSION · p. 16The 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.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ A. Filtered Back Projection · p. 7In 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.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Study design and conductreasoning§ I. INTRODUCTION · p. 3Training is possible from real data without oracle knowledge because high-view FBP reconstructions are used for training.
“We use high-view FBP reconstructions for training, meaning that training is possible from real data (without oracle knowledge).”
Quote in the paperSubstantial claim- Rests on an assumption: High-view FBP reconstructions can serve as ground truth for training and evaluation.
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductcitation§ B. Training Procedure · p. 10The FBPConvNet training clips the computed gradients to a fixed range to prevent the divergence of the cost function.
“We clip the computed gradients to a fixed range to prevent the divergence of the cost function [27], [46].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [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 in the free run.
- cites [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
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductcitation§ B. Training Procedure · p. 10The FBPConvNet training uses flip-flop data augmentation in both horizontal and vertical directions to reduce overfitting.
“We use flip-flop data augmentation in both horizontal and vertical directions during the training phase to reduce overfitting [18].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [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. -
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ C. Iterative Inversion · p. 6Many other iterative methods for solving Eq. (5), including ADMM, FISTA, and SALSA, also rely on these basic building blocks.
“Many other iterate methods for solving Eq. (5), including ADMM [40], FISTA [41], and SALSA [42], also rely on these basic building blocks.”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites [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.
- cites [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 in the free run.
- cites [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
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone given§ B. Training Procedure · p. 10For the biomedical dataset, the test data is chosen from a different subject than the training set.
“In the case of the biomedical dataset, the test data is chosen from a different subject than the training set.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductreasoning§ B. Training Procedure · p. 10The TV method's parameters were selected by optimizing performance on the training set via a golden-section search.
“we instead simply select the parameters that optimize performance on the training set (via a golden-section search).”
Quote in the paperNot a substantial claimMay combine two claims.
Premisecitation§ I. INTRODUCTION · p. 3The class of normal-convolutional inverse problems includes denoising, deconvolution, MRI, X-ray CT, and diffraction tomography.
“The class trivially includes denoising and deconvolution, but also includes MRI [35], X-ray CT [13], [16], and diffraction tomography (DT).”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [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.
- cites [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 in the free run.
- cites [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
Not checked in the free run.
May combine two claims.
Premisecitation§ C. Iterative Inversion · p. 6In practice, inverse problems related with imaging are often ill-posed, which prohibits direct inversion because measurement noise causes severe perturbations in the solution.
“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.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [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 in the free run.
- cites [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
Not checked in the free run.
May combine two claims.
Premisenone given§ C. Iterative Inversion · p. 6The synthesis formulation of the inverse problem does not admit a closed form solution and is typically solved iteratively.
“This formulation does not admit a closed form solution, and, therefore, is typically solved iteratively.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Skip connection · p. 8The U-net's multilevel decomposition is critical for the 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.
“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 .”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone given§ B. Training Procedure · p. 10For the real data, the test data are obtained from the last z-slices with a gap of 25 slices left between testing and training data.
“The test data are obtained from the last z-slices with the gap of 25 slices left between testing and training data.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationreasoning§ VI. DISCUSSION · p. 16One advantage of the proposed method over iterative methods is that the iterative methods must explicitly impose regularization, while the FBPConvNet effectively learns a regularizer from the data.
“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.”
Quote in the paperSubstantial claim
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?
U-net could effectively produce noiseless CT images from the subsampled sinogram.
“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]
The Experiments and Results section (p. 9) tests FBPConvNet on subsampled CT sinograms, and the Biomedical Dataset results (p. 13) report satisfactory removal of streaking artifacts and improved SNR. The network uses a modified U-net, but the paper does not claim its output is noiseless; the Discussion (p. 16) notes that artifacts can remain. (LLM, conf=0.88)
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.”
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Self-citationAlternating Dual Updates Algorithm for X-ray CT Reconstruction on the GPU
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MethodFast 3D reconstruction method for differential phase contrast X-ray CT
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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 · see citing works
“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 · see citing works
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 · see citing works
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 1,482 · see citing works
“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 1,402 · see citing works
“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 1,412 · see citing works
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 1,073 · see citing works
“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 · see citing works
“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 · see citing works
“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 · see citing works
“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 879 · see citing works
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 945 · see citing works
“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 792 · see citing works
Learned Primal-Dual Reconstruction
Adler, J., & Öktem, O. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2799231 · Cited by 870 · see citing works
“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 739 · see citing works
“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 710 · see citing works
Solving inverse problems using data-driven models
Arridge, S., Maaß, P., Öktem, O., & Schönlieb, C. (2019) · Acta Numerica · doi:10.1017/s0962492919000059 · Cited by 691 · see citing works
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 672 · see citing works
“…(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 651 · see citing works
Singh, D., Kumar, V., Vaishali, & Kaur, M. (2020) · European Journal of Clinical Microbiology & Infectious Diseases · doi:10.1007/s10096-020-03901-z · Cited by 647 · see citing works
“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 769 · see citing works
“[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 614 · see citing works
“[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 · see citing works
“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 620 · see citing works
“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 · see citing works
“, 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 · see citing works
“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 591 · see citing works
“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 · see citing works
“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 · see citing works
“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., & Man, B. D. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-00273-z · Cited by 560 · see citing works
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 · see citing works
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 658 · see citing works
“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 528 · see citing works
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 502 · see citing works
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 · see citing works
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 532 · see citing works
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 493 · see citing works
“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., Kutyniok, G., & Caire, G. (2021) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2021.3054977 · Cited by 498 · see citing works
“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 · see citing works
“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 452 · see citing works
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 451 · see citing works
“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 442 · see citing works
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 433 · see citing works
“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 · see citing works
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 415 · see citing works
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 460 · see citing works
“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 · see citing works
“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 405 · see citing works
“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 379 · see citing works
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 · see citing works
“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 · see citing works
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 · see citing works
“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 · see citing works
“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 355 · see citing works
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 · see citing works
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 324 · see citing works
“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 · see citing works
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 · see citing works
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 336 · see citing works
“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 · see citing works
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 · see citing works
“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 · see citing works
“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 294 · see citing works
“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 335 · see citing works
“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 305 · see citing works
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 284 · see citing works
“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 278 · see citing works
“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 289 · see citing works
“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 · see citing works
“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 265 · see citing works
“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 · see citing works
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 294 · see citing works
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 288 · see citing works
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 266 · see citing works
“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 · see citing works
“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 363 · see citing works
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 273 · see citing works
“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 244 · see citing works
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 · see citing works
“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 · see citing works
“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 · see citing works
“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 · see citing works
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 · see citing works
“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 · see citing works
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 231 · see citing works
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 · see citing works
“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 242 · see citing works
“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 230 · see citing works
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 228 · see citing works
“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 222 · see citing works
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 216 · see citing works
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 233 · see citing works
“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., et al. (2022) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2022.3218801 · Cited by 211 · see citing works
“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 · see citing works
“[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 · see citing works
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 208 · see citing works
Review of Vibration-Based Structural Health Monitoring Using Deep Learning
Toh, G., & Park, J. (2020) · Applied Sciences · doi:10.3390/app10051680 · Cited by 209 · see citing works
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 · see citing works
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 · see citing works
“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 · see citing works
“…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
- 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 · 2016: 1 · 2012: 1
- 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
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