The DOI matches its Crossref record; 74 of the 81 references it cites were found in a registry or an index; 2 of the 26 sources its claims cite were checked for support.
Learning Deep CNN Denoiser Prior for Image Restoration
Open accessAbstract
Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and drawbacks, e.g., model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming with sophisticated priors for the purpose of good performance, in the meanwhile, discriminative learning methods have fast testing speed but their application range is greatly restricted by the specialized task. Recent works have revealed that, with the aid of variable splitting techniques, denoiser prior can be plugged in as a modular part of model-based optimization methods to solve other inverse problems (e.g., deblurring). Such an integration induces considerable advantage when the denoiser is obtained via discriminative learning. However, the study of integration with fast discriminative denoiser prior is still lacking. To this end, this paper aims to train a set of fast and effective CNN (convolutional neural network) denoisers and integrate them into model-based optimization method to solve other inverse problems. Experimental results demonstrate that the learned set of denoisers can not only achieve promising Gaussian denoising results but also can be used as prior to deliver good performance for various low-level vision applications.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper trains a set of fast CNN Gaussian denoisers and uses them as modular priors inside a half-quadratic splitting optimization framework to solve image deblurring and super-resolution. Experiments show competitive denoising accuracy and flexible restoration performance across tasks without task-specific retraining.
Key findings
- The proposed CNN denoiser improves gray-image denoising on BSD68 over BM3D, WNNM, TNRD, and MLP: at σ=15 it reaches 31.63 dB, at σ=25 it reaches 29.15 dB, and at σ=50 it reaches 26.19 dB.
- For color denoising on BSD68, the proposed denoiser consistently beats CBM3D, e.g. 40.36 vs. 40.24 dB at noise level 5, 31.16 vs. 30.71 dB at 25, and 27.86 vs. 27.38 dB at 50.
- The learned denoisers can be inserted into a model-based optimization method to handle deblurring and single-image super-resolution; for example, on the Leaves deblurring case with Gaussian blur σ=1.6 and noise level 2, the proposed method reports 29.78 dB versus 26.95 dB for IDDBM3D and 27.50 dB for NCSR.
- Runtime is competitive: for a 256×256 image with noise level 25, the 24-feature-map version takes 0.10 s on CPU and 0.006 s on GPU, while BM3D takes 0.66 s on CPU and TNRD takes 0.47 s on CPU / 0.010 s on GPU.
Methods
- The authors design a seven-layer CNN denoiser using dilated convolutions with dilation factors 1, 2, 3, 4, 3, 2, 1; middle layers use 64 feature maps, and the effective receptive field is 33×33.
- Training uses 400 BSD images, 400 ImageNet validation images, and 4,744 Waterloo Exploration Database images, cropped into 35×35 patches with N = 256×4,000 patches; Adam is used with residual learning and batch normalization.
- A set of 25 denoisers is trained for gray images and 25 for color images over noise levels from 0 to 50 in steps of 2; these denoisers are integrated into a half-quadratic splitting scheme, where the regularization subproblem becomes a Gaussian denoising step.
Limitations
- The paper states that future work includes reducing the number of CNN denoisers and iterations, extending the framework to inpainting and blind deblurring, and using multiple complementary priors.
- The experimental evaluation is limited to denoising, non-blind deblurring, and super-resolution; inpainting and blind deblurring are not tested.
- The authors note that comparisons with SRCNN and VDSR for non-bicubic super-resolution are unfair because those methods were trained for bicubic degradation, which is evident from the reported setup rather than presented as a limitation of the proposed method.
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25 Own interpretation · 16 Own result · 10 No basis given · 9 No full text of the sources · 3 Sources not found · 3 Own method · 2 Not checked yet · 1 Supported · 1 Not supported · accuracy not yet measured
At least one cited source doesn’t support this claim or points to a different paper, and none confirmed it — see the verdicts below.
In the paper
“Note that SRCNN and VDSR are trained with bicubic blur kernel, thus it is unfair to use their models to super-resolve the low-resolution image with Gaussian kernel.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.3. Single Image Super-Resolution
What the sources say
- Disputedcites [21] 21. C. Dong, C. C. Loy, K. He, and X. Tang. Image super-resolution using deep convolutional networks. IEEE transactions on Pattern Analysis and Machine Intelligence, 38(2):295-307, 2016. 2, 7 sourceExperimental — accuracy not yet measured
Section 3.3 (p. 5) says SRCNN training samples are blurred with a Gaussian kernel; bicubic interpolation is a later upscaling step, not the blur kernel. Section 4.4.1 (p. 9) also describes training a separate SRCNN network with a different Gaussian kernel for comparison. The paper does not address VDSR's training. (LLM, conf=0.87)
Checked by a reasoning model — may be wrong.
- Not checked — no full text of the sourcecites [35] 35. J. Kim, J. K. Lee, and K. M. Lee. Accurate image super- resolution using very deep convolutional networks. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1646-1654, 2016. 4, 7 source
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In the paper
“Experimental results demonstrate that the learned set of denoisers can not only achieve promising Gaussian denoising results but also can be used as prior to deliver good performance for various low-level vision applications.”
- Also stated in: § 1. Introduction · boosted
“Extensive experiments on classical IR problems, including deblurring and super-resolution, have demonstrated the merits of integrating flexible model-based optimization methods and fast CNN-based discriminative learning methods.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Abstract
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- Also stated in: § 1. Introduction · boosted
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In the paper
“we empirically find it also can enable fast transfer from one model to another with different noise level.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
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In the paper
“However, if the size of the training patch is smaller than the receptive field, the performance would decrease.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
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In the paper
“However, the proposed CNN denoiser can have a PSNR gain of about 0.2dB over those three methods.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“We empirically find that using training samples with small size can help avoid boundary artifacts.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
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In the paper
“We can see that the proposed denoiser is very competitive in both CPU and GPU implementation.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Due to the iterative scheme, it turns out the noise level range of [0, 50] is enough to handle various image restoration problems.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
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In the paper
“it can be seen that the proposed denoiser consistently outperforms CBM3D by a large margin.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“It can be seen that WNNM, MLP and TNRD can outperform BM3D by about 0.3dB in PSNR.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
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Every source the paper cites for this claim was checked and supports it.
In the paper
“it has been pointed out that the combination of batch normalization and residual learning is particularly helpful for Gaussian denoising since they are beneficial to each other.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
What the sources say
- Supportedcites [65] 65. K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang. Be- yond a Gaussian denoiser: Residual learning of deep CNN for image denoising. IEEE Transactions on Image Process- ing, 2017. 4 source
Section C (pp. 4–5) says residual learning and batch normalization can benefit each other in Gaussian denoising, and reports faster convergence and better denoising performance when combined. Section B (p. 3) also describes their integration as producing fast, stable training and better denoising performance. (LLM, conf=0.95)
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In the paper
“It is worth emphasizing that the proposed denoiser with 24 feature maps of each layer has a comparable PSNR of 28.94dB to TNRD but delivers a faster speed.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
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In the paper
“We empirically find using large dataset does not improve the PSNR results of BSD68 dataset [50] but can slightly improve the performance of other testing images.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
What the sources say
- Not checked — no full text of the sourcecites [50] 50. S. Roth and M. J. Black. Fields of experts. International Journal of Computer Vision, 82(2):205-229, 2009. 1, 4, 5 source
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In the paper
“It turns out that our designed model can have an average P-SNR of 29.15dB on BSD68 dataset [50], which is much better than 28.94dB of 7 layers network with traditional 3×3 convolution filter and very close to 29.20dB of 16 layers network.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.2. The Proposed CNN Denoiser
What the sources say
- Not checked — no full text of the sourcecites [50] 50. S. Roth and M. J. Black. Fields of experts. International Journal of Computer Vision, 82(2):205-229, 2009. 1, 4, 5 source
plainn = 2- Asserted: passes — The authors put it forward as true.
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In the paper
“As an example for the testing speed comparison, our method can super-resolve the Butterfly image in 0.5 second on GPU and 12 seconds on CPU, whereas NCSR spends 198 seconds on CPU.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.3. Single Image Super-Resolution
plainSingle case- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: The low-resolution image can be modeled by a blurring and subsequent down-sampling operation on a high-resolution 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
“We can see that IDDBM3D, NCSR and MLP tend to smooth the edges and generate color artifacts.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.2. Image Deblurring
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The convolution is carried out with circular boundary conditions.
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
“First, although S-RCNN and VDSR achieve promising results to tackle the case with bicubic kernel, their performance deteriorates seriously when the low-resolution image are not generated by bicubic kernel (see Figure 4).”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.3. Single Image Super-Resolution
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: The low-resolution image can be modeled by a blurring and subsequent down-sampling operation on a high-resolution 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 contrast, the proposed method can recover image sharpness and naturalness.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.2. Image Deblurring
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The convolution is carried out with circular boundary conditions.
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
“Third, both of the gray and color CNN denoiser prior based optimization methods can produce promising results.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.3. Single Image Super-Resolution
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: The low-resolution image can be modeled by a blurring and subsequent down-sampling operation on a high-resolution 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
“Third, CNN exploits the external prior which is complementary to the internal prior of many existing denoisers such as BM3D.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.1. Why Choose CNN Denoiser?
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In the paper
“model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming with sophisticated priors for the purpose of good performance”
- Also stated in: § 1. Introduction · plain
“model-based optimization methods are usually timeconsuming with sophisticated priors for the purpose of good performance [27].”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Abstract
What the sources say
- Not checked — no full text of the sourcecites [27] 27. Q. Gao and S. Roth. How well do filter-based MRFs model natural images? In Joint DAGM (German Association for Pattern Recognition) and OAGM Symposium, pages 62-72, 2012. 2 source
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- Also stated in: § 1. Introduction · plain
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
“Second, CNN exhibits powerful prior modeling capacity with deep architecture.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.1. Why Choose CNN Denoiser?
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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
“First, the inference of CNN is very efficient due to the parallel computation ability of GPU.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.1. Why Choose CNN Denoiser?
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
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
“Especially noteworthy is the number of the denoisers which is much less than that of learning different models for different degradations.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
plain- Asserted: passes — The authors put it forward as true.
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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
“discriminative learning methods have fast testing speed but their application range is greatly restricted by the specialized task.”
- Also stated in: § 1. Introduction · plain
“discriminative learning methods are usually restricted by specialized tasks.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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- Also stated in: § 1. Introduction · plain
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
“Such a good compromise between speed and performance over TNRD is properly attributed to the following three reasons.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“and it is preferable to jointly handle RGB channels.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.1. Why Choose CNN Denoiser?
What the sources say
- Not matchedcites [42] 42. T. Miyata. Inter-channel relation based vectorial total varia- tion for color image recovery. In IEEE International Confer- ence on Image Processing,, pages 2251-2255, 2015. 3
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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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
“To make a further comparison with TNRD under similar PSNR performance, we additionally provide the run time of the proposed denoiser where each middle layer has 24 feature maps.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.1. Image Denoising
plain- Asserted: passes — The authors put it forward as true.
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Probably 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
“the denoiser here just acts its own role regardless of the noise type and noise level of the image to be denoised.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > Using Batch Normalization and Residual Learning to Accelerate Training.
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“To show the advantage of our design over the above two cases, we have trained three different models on noise level 25 with same training settings.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 3.2. The Proposed CNN Denoiser
plaindirectn = 2- Asserted: passes — The authors put it forward as true.
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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
“It is worthy noting that the iterative regularization step of methods such as NCSR and WNNM actually corresponds to solving Eqn.(6a).”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.3. Single Image Super-Resolution
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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 number of iterations is set to 30 as we find it is large enough to obtain a satisfying performance.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 4.2. Image Deblurring
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- The authors state this as an assumption: The convolution is carried out with circular boundary conditions.
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
“On the other hand, different from discriminative learning methods which are specialized for certain image restoration tasks, the proposed deep CNN denoiser prior based optimization method is flexible in handling various tasks while can produce very favorable results.”
§ Learning Deep CNN Denoiser Prior for Image Restoration > 5. Conclusion
plain- Asserted: passes — The authors put it forward as true.
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The paper relies on this without support.
The study of integration with fast discriminative denoiser prior is still lacking.
“However, the study of integration with fast discriminative denoiser prior is still lacking.”
“However, to the best of our knowledge, the study of integration with discriminative denoiser is still lacking.”
The authors state this as an assumption.
The convolution is carried out with circular boundary conditions.
“In addition, we assume the convolution is carried out with circular boundary conditions.”
The paper relies on this without support.
The low-resolution image can be modeled by a blurring and subsequent down-sampling operation on a high-resolution one.
“In general, the low-resolution (LR) image can be modeled by a blurring and subsequent down-sampling operation on a high-resolution one.”
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 1×
“Thus, using 3×3 filter with a large depth is popularized in existing CNN network design [30, 35, 56].”
MethodVery Deep Convolutional Networks for Large-Scale Image Recognition
Simonyan, K., & Zisserman, A. (2014) · arXiv · doi:10.48550/arxiv.1409.1556 · Cited by 114,148 · cited 1×
“However, increasing the filter size would not only introduce more parameters but also increase the computational burden [53].”
BackgroundImageNet 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 1×
“Particularly, several CNN techniques, including Rectifier Linear Units (ReLU) [37], batch normalization [32], Adam [36], dilated convolution [63] are adopted into the network design or training.”
MethodAdam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946 · cited 5×
“Particularly, several CNN techniques, including Rectifier Linear Units (ReLU) [37], batch normalization [32], Adam [36], dilated convolution [63] are adopted into the network design or training.”
MethodInfluentialImageNet: A large-scale hierarchical image database
Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., & Fei-Fei, L. (2009) · 2009 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2009.5206848 · Cited by 65,333 · cited 1×
“Hence, instead of training on a small dataset consisting of 400 Berkeley segmentation dataset (BSD) images of size 180×180 [13], we collect a large dataset which includes 400 BSD images, 400 selected images from validation set of ImageNet database [20] and 4,744 images of Waterloo Exploration Database [40].”
MethodGoing deeper with convolutions
Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., & Rabinovich, A. (2015) · 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2015.7298594 · Cited by 48,562 · cited 1×
“Thus, using 3×3 filter with a large depth is popularized in existing CNN network design [30, 35, 56].”
MethodBatch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
Ioffe, S., & Szegedy, C. (2015) · arXiv · doi:10.48550/arxiv.1502.03167 · Cited by 27,818 · cited 2×
“Particularly, several CNN techniques, including Rectifier Linear Units (ReLU) [37], batch normalization [32], Adam [36], dilated convolution [63] are adopted into the network design or training.”
BackgroundMethodBoyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Boyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,917
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952 · cited 1×
“Note that this property can be also employed in other optimization methods ( e.g ., iterative shrink-age/thresholding algorithms ISTA [4, 14] and FISTA [3]) as long as there involves a denoising subproblem.”
Image Super-Resolution Using Deep Convolutional Networks
Dong, C., Loy, C. C., He, K., & Tang, X. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2015.2439281 · Cited by 10,105 · cited 4×
“By iteratively updating a back-projection step and a CBM3D denoising step, the method has an encouraging performance for its PSNR improvement over SRCNN [21].”
MethodInfluentialImage denoising by sparse 3-D transform-domain collaborative filtering
Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901238 · Cited by 9,283 · cited 3×
“, BM3D [17] and WNNM [29]), two discriminative learning methods (i.”
MethodBeyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
Zhang, K., Zuo, W., Chen, Y., Meng, D., & Zhang, L. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2662206 · Cited by 8,983
Self-citationAccurate Image Super-Resolution Using Very Deep Convolutional Networks
Kim, J., Lee, J. K., & Lee, K. M. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.182 · Cited by 7,870 · cited 2×
“…SISR method is compared with five state-of-the-art methods, including two CNN-based discriminative learning methods ( i.e ., SRCNN [21] and VDSR [35]), one statistical prediction model based discriminative learning method [45] which we refer to as SPMSR, one model based optimization method (…”
MethodMulti-scale context aggregation by dilated convolutions
Yu, F., & Koltun, V. (2015) · arXiv · doi:10.48550/arxiv.1511.07122 · Cited by 7,738
A Non-Local Algorithm for Image Denoising
Buades, A., Coll, B., & Morel, J.-M. (2005) · 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) · doi:10.1109/cvpr.2005.38 · Cited by 7,616 · cited 1×
“Existing denoiser priors that have been adopted in model-based optimization methods to solve other inverse problems include total variation (TV) [10, 43], Gaussian mixture models (GMM) [66], K-SVD [25], non-local means [7] and BM3D [17].”
MethodImage Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
Elad, M., & Aharon, M. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.881969 · Cited by 5,321 · cited 2×
“For example, TV can create watercolor-like artifacts; K-SVD denoiser prior suffers high computational burden; non-local means and BM3D denoiser priors may over-smooth the irregular structures if the image does not exhibit self-similarity property.”
MethodA First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Chambolle, A., & Pock, T. (2011) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-010-0251-1 · Cited by 4,336 · cited 1×
“, the primaldual algorithm [11], to decouple fidelity term and regularization term.”
BackgroundDeep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., & Sun, J. (2015) · arXiv · doi:10.48550/arxiv.1512.03385 · Cited by 4,196
Bayesian-Based Iterative Method of Image Restoration*
Richardson, W. H. (1972) · Journal of the Optical Society of America · doi:10.1364/josa.62.000055 · Cited by 4,160 · cited 1×
“Image restoration (IR) has been a long-standing problem for its highly practical value in various low-level vision applications [1, 9, 47].”
BackgroundParikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
chambolle (2004) · doi:10.1023/b:jmiv.0000011321.19549.88 · Cited by 3,227
Signal Recovery by Proximal Forward-Backward Splitting
Combettes, P. L., & Wajs, V. R. (2005) · Multiscale Modeling and Simulation · doi:10.1137/050626090 · Cited by 2,681 · cited 2×
“, iterative shrinkage/thresholding algorithms ISTA [4, 14] and FISTA [3]) as long as there involves a denoising subproblem.”
MethodMatConvNet: Convolutional Neural Networks for MATLAB
Vedaldi, A., & Lenc, K. (2015) · Proceedings of the 23rd ACM international conference on Multimedia · doi:10.1145/2733373.2807412 · Cited by 2,444 · cited 1×
“The denoiser models are trained in Matlab (R2015b) environment with MatConvNet package [60] and an Nvidia Titan X GPU.”
MethodWeighted Nuclear Norm Minimization with Application to Image Denoising
Gu, S., Zhang, L., Zuo, W., & Feng, X. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.366 · Cited by 2,316
Self-citationKuybeda, O., Frank, G. A., Bartesaghi, A., Borgnia, M. J., Subramaniam, S., & Sapiro, G. (2012) · Journal of Structural Biology · doi:10.1016/j.jsb.2012.10.010 · Cited by 2,200 · cited 1×
“(6b)) are difficult or time-consuming to optimize, then using an inexact but fast subproblem solution may accelerate the convergence [39, 66].”
BackgroundA New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.909319 · Cited by 2,064 · cited 2×
“, iterative shrinkage/thresholding algorithms ISTA [4, 14] and FISTA [3]) as long as there involves a denoising subproblem.”
MethodAn Iterative Regularization Method for Total Variation-Based Image Restoration
Osher, S., Burger, M., Goldfarb, D., Xu, J., & Yin, W. (2005) · Multiscale Modeling & Simulation · doi:10.1137/040605412 · Cited by 1,787 · cited 1×
“Existing denoiser priors that have been adopted in model-based optimization methods to solve other inverse problems include total variation (TV) [10, 43], Gaussian mixture models (GMM) [66], K-SVD [25], non-local means [7] and BM3D [17].”
MethodSparse Representation for Color Image Restoration
Mairal, J., Elad, M., & Sapiro, G. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.911828 · Cited by 1,716 · cited 1×
“However, existing methods mainly focus on modeling gray image prior and there are only a few works concentrating on modeling color image prior (see, e.g ., [16, 41, 46]).”
MethodBanham, M. R., & Katsaggelos, A. K. (1997) · IEEE Signal Processing Magazine · doi:10.1109/79.581363 · Cited by 1,679
From learning models of natural image patches to whole image restoration
Zoran, D., & Weiss, Y. (2011) · 2011 International Conference on Computer Vision · doi:10.1109/iccv.2011.6126278 · Cited by 1,522
Nonlocally Centralized Sparse Representation for Image Restoration
Dong, W., Zhang, L., Shi, G., & Li, X. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2235847 · Cited by 1,505 · cited 4×
“s, we choose one discriminative method named MLP [52] and three model based optimization methods, including IDDBM3D [19], NCSR [22] and EPLL.”
MethodInfluentialSelf-citationA+: Adjusted Anchored Neighborhood Regression for Fast Super-Resolution
Timofte, R., Smet, V. D., & Gool, L. V. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-16817-3_8 · Cited by 1,470
Chen, Y., & Pock, T. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2596743 · Cited by 1,344 · cited 3×
“On the contrary, discriminative learning methods try to learn the prior parameters Θ and a compact inference through an optimization of a loss function on a training set containing degraded-clean image pairs [2, 13, 51, 55, 57].”
BackgroundMethodImage denoising: Can plain neural networks compete with BM3D?
Burger, H. C., Schuler, C. J., & Harmeling, S. (2012) · 2012 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2012.6247952 · Cited by 1,325
Understanding and evaluating blind deconvolution algorithms
Levin, A., Weiss, Y., Durand, F., & Freeman, W. T. (2009) · 2009 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2009.5206815 · Cited by 1,208 · cited 1×
“6 and the first two of the eight real blur kernels from [38].”
BackgroundPlug-and-Play priors for model based reconstruction
Venkatakrishnan, S. V., Bouman, C. A., & Wohlberg, B. (2013) · 2013 IEEE Global Conference on Signal and Information Processing · doi:10.1109/globalsip.2013.6737048 · Cited by 1,178 · cited 3×
“Here we note that, prior to [61], a similar idea of plug-and-play is also mentioned in [66] where a half quadratic splitting (HQS) method was proposed for image denoising, deblurring and inpainting.”
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank MatricesPreprint
Lin, Z., Chen, M., & Ma, Y. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1009.5055 · Cited by 1,177
Nonlinear image recovery with half-quadratic regularization
Geman, D., & Yang, C. (1995) · IEEE Transactions on Image Processing · doi:10.1109/83.392335 · Cited by 1,000 · cited 1×
“Fortunately, with the aid of variable splitting techniques, such as alternating direction method of multipliers (ADMM) method [5] and halfquadratic splitting (HQS) method [28], it is possible to deal with fidelity term and regularization term separately [44], and particularly, the regularization term only corresponds…”
MethodThe Little Engine That Could: Regularization by Denoising (RED)
Romano, Y., Elad, M., & Milanfar, P. (2017) · SIAM Journal on Imaging Sciences · doi:10.1137/16m1102884 · Cited by 934 · cited 1×
“Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
BackgroundPlug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications
Chan, S. H., Wang, X., & Elgendy, O. A. (2017) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2016.2629286 · Cited by 904 · cited 1×
“Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
BackgroundRoth, S., & Black, M. J. (2009) · International Journal of Computer Vision · doi:10.1007/s11263-008-0197-6 · Cited by 847 · cited 3×
“We empirically find using large dataset does not improve the PSNR results of BSD68 dataset [50] but can slightly improve the performance of other testing images.”
BackgroundMethodInfluential(2008) · Cited by 838
Deep Convolutional Neural Network for Image Deconvolution
Li, X., Ren, J., Liu, C., & Jia, J. (2014) · Rare & Special e-Zone (The Hong Kong University of Science and Technology) · Cited by 836
An Algorithm for Total Variation Minimization and Applications
Chambolle, A. (2004) · Journal of Mathematical Imaging and Vision · doi:10.1023/b:jmiv.0000011325.36760.1e · Cited by 835
Motion Analysis for Image Enhancement: Resolution, Occlusion, and Transparency
Irani, M., & Peleg, B. (1993) · Journal of Visual Communication and Image Representation · doi:10.1006/jvci.1993.1030 · Cited by 806 · cited 1×
“Inspired by the method proposed in [24] which iteratively updates a back-projection [33] step and a denoising step for SISR, we use the following back-projection iteration to solve Eqn.”
MethodWaterloo Exploration Database: New Challenges for Image Quality Assessment Models
Ma, K., Duanmu, Z., Wu, Q., Wang, Z., Yong, H., Li, H., & Zhang, L. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2631888 · Cited by 789 · cited 1×
“Hence, instead of training on a small dataset consisting of 400 Berkeley segmentation dataset (BSD) images of size 180×180 [13], we collect a large dataset which includes 400 BSD images, 400 selected images from validation set of ImageNet database [20] and 4,744 images of Waterloo Exploration Database [40].”
MethodSelf-citationBM3D Frames and Variational Image Deblurring
Danielyan, A., Katkovnik, V., & Egiazarian, K. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2176954 · Cited by 611 · cited 5×
“In the following experiments, we simply plug the color denoisers into the HQS framework, whereas we separately handle each color channel for IDDBM3D and MLP. Note that MLP trained a specific model for the Gaussian blur kernel with noise level 2.”
MethodInfluentialShrinkage Fields for Effective Image Restoration
Schmidt, U., & Roth, S. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.349 · Cited by 543
Sondhi, M. M. (1978) · IEEE Transactions on Acoustics Speech and Signal Processing · doi:10.1109/tassp.1978.1163057 · Cited by 539
Dabov, K., Foi, A., Katkovnik, V. Y., et al. (2007) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2007.4378954 · Cited by 482 · cited 2×
“Perhaps the most successful color image prior modeling method is CBM3D [16].”
Method1 BM3D frames and variational image deblurring
Danielyan, A., Katkovnik, V., Egiazarian, K., & Member, S. (2012) · Cited by 414
A Statistical Prediction Model Based on Sparse Representations for Single Image Super-Resolution
Peleg, T., & Elad, M. (2014) · IEEE Transactions on Image Processing · doi:10.1109/tip.2014.2305844 · Cited by 406 · cited 3×
“, SRCNN [21] and VDSR [35]), one statistical prediction model based discriminative learning method [45] which we refer to as SPMSR, one model based optimization method (i.”
MethodVideo Denoising By Sparse 3D Transform-Domain Collaborative Filtering
Dabov, K., Foi, A., & Egiazarian, K. (2007) · doi:10.5281/zenodo.40233 · Cited by 384
Image Denoising Via Learned Dictionaries and Sparse representation
Elad, M., & Aharon, M. (2006) · 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.2006.142 · Cited by 384
Image Denoising Using the Higher Order Singular Value Decomposition
Rajwade, A. V., Rangarajan, A., & Banerjee, A. (2012) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.140 · Cited by 375
Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation
Sreehari, S., Venkatakrishnan, S. V., Wohlberg, B. E., Buzzard, G. T., Drummy, L. F., Simmons, J. P., & Bouman, C. A. (2016) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2016.2599778 · Cited by 358
Blind image deconvolution: theory and applications
Campisi, P., & Egiazarian, K. (2007) · Cited by 348
A Machine Learning Approach for Non-blind Image Deconvolution
Schuler, C. J., Burger, H. C., Harmeling, S., & Scholkopf, B. (2013) · 2013 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2013.142 · Cited by 319 · cited 7×
“It can be seen that WNNM, MLP and TNRD can outperform BM3D by about 0.3dB in PSNR.”
MethodInfluentialFlexISP: a flexible camera image processing framework
Heide, F., Steinberger, M., Tsai, Y.-T., Rouf, M., Pająk, D., Reddy, D., Gallo, O., Liu, J., Heidrich, W., Egiazarian, K., et al. (2014) · ACM Transactions on Graphics · doi:10.1145/2661229.2661260 · Cited by 298 · cited 2×
“In [31], the authors used an alternative to ADMM and HQS, i.e ., the primal-dual algorithm [11], to decouple fidelity term and regularization term.”
MethodDeep Network Cascade for Image Super-resolution
Cui, Z., Chang, H., Shan, S., Zhong, B., & Chen, X. (2014) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-10602-1_4 · Cited by 255 · cited 2×
“, bicubic downsampling (default setting of Matlab function imresize) with two scale factors 2 and 3 [15, 21] and blurring by Gaussian kernel of size 7×7 with standard deviation 1.”
BackgroundAccurate Blur Models vs. Image Priors in Single Image Super-resolution
Efrat, N., Glasner, D., Apartsin, A., Nadler, B., & Levin, A. (2013) · 2013 IEEE International Conference on Computer Vision · doi:10.1109/iccv.2013.352 · Cited by 200
Poisson inverse problems by the Plug-and-Play scheme
Rond, A., Giryes, R., & Elad, M. (2016) · Journal of Visual Communication and Image Representation · doi:10.1016/j.jvcir.2016.09.009 · Cited by 132 · cited 1×
“Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
BackgroundTraining an Active Random Field for Real-Time Image Denoising
Barbu, A. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2028254 · Cited by 105 · cited 1×
“On the contrary, discriminative learning methods try to learn the prior parameters Θ and a compact inference through an optimization of a loss function on a training set containing degraded-clean image pairs [2, 13, 51, 55, 57].”
BackgroundTurning a denoiser into a super-resolver using plug and play priors
Brifman, A., Romano, Y., & Elad, M. (2016) · 2016 IEEE International Conference on Image Processing (ICIP) · doi:10.1109/icip.2016.7532589 · Cited by 91 · cited 1×
“Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
BackgroundImage restoration and reconstruction using variable splitting and class-adapted image priors
Teodoro, A. M., Bioucas‐Dias, J. M., & Figueiredo, M. A. T. (2016) · doi:10.1109/icip.2016.7533014 · Cited by 73 · cited 1×
“Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
BackgroundImage Denoising By Non-Local Averaging
Buades, A. R., Coll, B., & Morel, J. (2006) · doi:10.1109/icassp.2005.1415332 · Cited by 65
Single image super-resolution via BM3D sparse coding
Egiazarian, K., & Katkovnik, V. (2015) · 2015 23rd European Signal Processing Conference (EUSIPCO) · doi:10.1109/eusipco.2015.7362905 · Cited by 58 · cited 3×
“Inspired by the method proposed in [24] which iteratively updates a back-projection [33] step and a denoising step for SISR, we use the following back-projection iteration to solve Eqn.”
BackgroundMethodUtilizing Variational Optimization to Learn Markov Random Fields
Tappen, M. F. (2007) · 2007 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2007.383037 · Cited by 54 · cited 1×
“On the contrary, discriminative learning methods try to learn the prior parameters Θ and a compact inference through an optimization of a loss function on a training set containing degraded-clean image pairs [2, 13, 51, 55, 57].”
BackgroundSeparable Markov Random Field Model and Its Applications in Low Level Vision
Sun, J. Z., & Tappen, M. F. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2208981 · Cited by 36 · cited 1×
“On the contrary, discriminative learning methods try to learn the prior parameters Θ and a compact inference through an optimization of a loss function on a training set containing degraded-clean image pairs [2, 13, 51, 55, 57].”
Zhang, K., Zhou, X., Zhang, H., & Zuo, W. (2015) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-24075-6_65 · Cited by 24 · cited 1×
“This makes the learned model deteriorates seriously when the blur kernel adopted in training deviates from the real one [23, 64].”
BackgroundSelf-citationHow Well Do Filter-Based MRFs Model Natural Images?
Gao, Q., & Roth, S. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-32717-9_7 · Cited by 22
Inter-channel relation based vectorial total variation for color image recovery
Miyata, T. (2015) · doi:10.1109/icip.2015.7351202 · Cited by 8 · cited 1×
“While CBM3D is promising for color image denoising, it has been pointed out that the resulting transformed luminance-chrominance color channels still remain some correlation [42] and it is preferable to jointly handle RGB channels.”
BackgroundThe Little Engine that Could: Regularization by Denoising (RED)Preprint
Romano, Y., Elad, M., & Milanfar, P. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1611.02862 · Cited by 8
Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation
Sreehari, S., Venkatakrishnan, S. V., Wohlberg, B., et al. (2015) · arXiv · doi:10.48550/arxiv.1512.07331
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Cited by
Sorted by citations
Image Super-Resolution Using Very Deep Residual Channel Attention Networks
Zhang, Y., Li, K., Li, K., Wang, L., Zhong, B., & Fu, Y. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-01234-2_18 · Cited by 6,003
“We further apply our method to super-resolve images with blur-down (BD) degradation model, which is also commonly used recently [11,15,17].”
BackgroundMethodInfluentialSwinIR: Image Restoration Using Swin Transformer
Liang, J., Cao, J., Sun, G., Zhang, K., Gool, L. V., & Timofte, R. (2021) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw54120.2021.00210 · Cited by 5,150
“Dataset σ BM3D [14] DnCNN [90] IRCNN [91] FFDNet [92] DSNet [64] RPCNN [85] BRDNet [71] RNAN [96] RDN [98] IPT [9] DRUNet [88] SwinIR (ours)”
BackgroundMethodInfluentialSelf-citationResidual Dense Network for Image Super-Resolution
Zhang, Y., Tian, Y., Kong, Y., Zhong, B., & Fu, Y. (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.2018.00262 · Cited by 4,371
“Our RDN is compared with SPMSR [20], SRCNN [3], FSRCNN [4], VDSR [10], IRCNN G [38], and IRCNN C [38].”
BackgroundMethodResultInfluentialRestormer: Efficient Transformer for High-Resolution Image Restoration
Zamir, S. W., Arora, A., Khan, S., Hayat, M., Khan, F. S., & Yang, M. (2022) · 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/cvpr52688.2022.00564 · Cited by 4,737
FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising
Zhang, K., Zuo, W., & Zhang, L. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2839891 · Cited by 2,990
“In [9], dilated convolution is introduced to expand receptive field without the increase of network depth, resulting in a 7-layer denoising CNN.”
BackgroundInfluentialSelf-citation
Metadata
- Authors
- Zhang, K., Zuo, W., Gu, S., & Zhang, L.
- Affiliations
- Hong Kong Polytechnic University (HK)
- Harbin Institute of Technology (CN)
- Venue
- 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- Publisher
- IEEE
- Published
- 2017-07
- Pages
- 2808-2817
- OpenAlex
- W2613155248
- Cited by
- 2,116
- References
- 81
- Citations by year
- 2026: 80 · 2025: 191 · 2024: 248 · 2023: 293 · 2022: 272 · 2021: 338 · 2020: 297 · 2019: 240 · 2018: 135 · 2017: 10
- FWCI
- 49.67
- Type
- conference paper
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings (publishedVersion)
- PolyU Institutional Research Archive (Hong Kong Polytechnic University) (submittedVersion)
- TUScholarShare (Temple University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image Processing Techniques
- Physical Sciences › Engineering › Media Technology › Advanced Image Fusion Techniques
- Keywords
- image restoration, model-based optimization, discriminative learning, variable splitting, inverse problems, low-level vision, Gaussian denoising, image deblurring
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 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
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 ›
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