Abstract：In model-driven image denoising, prior regularization terms are required to be constructed in advance, resulting in high computational cost of dealing with optimization models. Data-driven methods possess superior performance and high efficiency due to the flexible architecture and powerful learning capability of neural networks, but their interpretability is insufficient. Therefore, truncated nuclear norm based unfolding network for image denoising is proposed and combined with the model-driven method based on truncated nuclear norm and image denoising in low-rank matrix recovery. Each iteration is regarded as a stage of the unfolding network. Singular value operators are learned with the help of neural networks to solve the problem of expensive computation of singular value decomposition in traditional iterative algorithms. Each of the stages is connected to form an end-to-end trainable unfolding network. The effectiveness of the proposed network is verified by the experiments on multiple datasets of image denoising.
[1] SAGHEER S V M, GEORGE S N. A Review on Medical Image Denoising Algorithms. Biomedical Signal Processing and Control, 2020. DOI: 10.1016/j.bspc.2020.102036. [2] MINNEN D, JANUSZEWSKI M, SHAPSON-COE A, et al. Denoi-sing-Based Image Compression for Connectomics[C/OL]. [2022-06-25]. https://www.biorxiv.org/content/10.1101/2021.05.29.445828v2.full.pdf. [3] CHEN H A, JIN Y, XU K, et al. Multiframe-to-Multiframe Network for Video Denoising. IEEE Transactions on Multimedia, 2021, 24: 2164-2178. [4] CHEN C, LIU Q D, JIN Y M, et al. Source-Free Domain Adaptive Fundus Image Segmentation with Denoised Pseudo-Labeling// Proc of the International Conference on Medical Image Computing and Computer-Assisted Intervention. Berlin, Germany: Springer, 2021: 225-235. [5] YANG X, YAN J C, LIAO W L, et al. SCRDet++: Detecting Small, Cluttered and Rotated Objects via Instance-Level Feature Denoising and Rotation Loss Smoothing. IEEE Transactions on Pa-ttern Analysis and Machine Intelligence, 2022. DOI: 10.1109/TPAMI.2022.3166956. [6] DE OLIVEIRA V A, CHABERT M, OBERLIN T, et al. Satellite Image Compression and Denoising with Neural Networks. IEEE Geoscience and Remote Sensing Letters, 2022, 19. DOI: 10.1109/LGRS.2022.3145992. [7] FENG X B, ZHANG W X, SU X Q, et al. Optical Remote Sensing Image Denoising and Super-Resolution Reconstructing Using Optimized Generative Network in Wavelet Transform Domain. Remote Sensing, 2021, 13(9). DOI: 10.3390/rs13091858. [8] WEN Y, GUO Z C, YAO W J, et al. Hybrid BM3D and PDE Fil-tering for Non-parametric Single Image Denoising. Signal Processing, 2021, 184. DOI: 10.1016/j.sigpro.2021.108049. [9] DABOV K, FOI A, KATKOVNIK V, et al. Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering. IEEE Transactions on Image Processing, 2007, 16(8): 2080-2095. [10] ZHANG K, ZUO W M, CHEN Y J, et al. Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising. IEEE Transactions on Image Processing, 2017, 26(7): 3142-3155. [11] KIM M, PARK J, KIM J.Learning Collaborative Policies to Solve NP-Hard Routing Problems// Proc of the 35th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2021: 10418-10430. [12] CANDÈS E J, RECHT B. Exact Matrix Completion via Convex Optimization. Foundations of Computational Mathematics, 2009, 9(6): 717-772. [13] HU Y, ZHANG D B, YE J P, et al. Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 35(9): 2117-2130. [14] YU T Y, LI S M, LU J T, et al. A Quantum Weak Signal Detection Method for Strengthening Target Signal Features under Strong White Gaussian Noise. Applied Sciences, 2022, 12(4). DOI: 10.3390/app12041878. [15] WANG S Q, CHEN Y Y, JIN Y, et al. Error-Robust Low-Rank Tensor Approximation for Multi-view Clustering. Knowledge-Based Systems, 2021, 215. DOI: 10.1016/j.knosys.2021.106745. [16] ZHANG H N, LIU L J, ZHOU H Y, et al. CMD: Controllable Matrix Decomposition with Global Optimization for Deep Neural Network Compression. Machine Learning, 2022, 111(3): 831-851. [17] FENG S, TANG S L, ZHAO C H, et al. A Hyperspectral Anomaly Detection Method Based on Low-Rank and Sparse Decomposition with Density Peak Guided Collaborative Representation. IEEE Transactions on Geoscience and Remote Sensing, 2021, 60. DOI: 10.1109/TGRS.2021.3054736. [18] LI L, LI W, DU Q, et al. Low-Rank and Sparse Decomposition with Mixture of Gaussian for Hyperspectral Anomaly Detection. IEEE Transactions on Cybernetics, 2020, 51(9): 4363-4372. [19] WRIGHT J, PENG Y G, MA Y, et al. Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization// Proc of the 22nd International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2009: 2080-2088. [20] TIAN R, SUN G L, LIU X C, et al. Sobel Edge Detection Based on Weighted Nuclear Norm Minimization Image Denoising. Electronics, 2021, 10(6). DOI: 10.3390/electronics10060655. [21] WEI Z L, FU N, JIANG S Y, et al. Parameter Measurement of LFM Signal with FRI Sampling and Nuclear Norm Denoising. IEEE Transactions on Instrumentation and Measurement, 2022, 71. DOI: 10.1109/TIM.2022.3158986. [22] GU S H, ZHANG L, ZUO W M, et al. Weighted Nuclear Norm Minimization with Application to Image Denoising// Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 2862-2869. [23] YE H L, LI H, CAO F L, et al. A Hybrid Truncated Norm Regularization Method for Matrix Completion. IEEE Transactions on Image Processing, 2019, 28(10): 5171-5186. [24] CAO F L, CHENG J Y, YE H L, et al. Recovering Low-Rank and Sparse Matrix Based on the Truncated Nuclear Norm. Neural Networks, 2017, 85: 10-20. [25] BENZ P, ZHANG C N, KARJAUV A, et al. Revisiting Batch Normalization for Improving Corruption Robustness// Proc of the IEEE Winter Conference on Applications of Computer Vision. Washington, USA: IEEE, 2021: 494-503. [26] ZHANG K, ZUO W M, ZHANG L.FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising. IEEE Transactions on Image Processing, 2018, 27(9): 4608-4622. [27] TIAN C W, XU Y, ZUO W M, et al. Designing and Training of a Dual CNN for Image Denoising. Knowledge-Based Systems, 2021, 226. DOI: 10.1016/j.knosys.2021.106949. [28] TIAN C W, XU Y, ZUO W M.Image Denoising Using Deep CNN with Batch Renormalization. Neural Networks, 2020, 121: 461-473. [29] TIAN C W, XU Y, LI Z Y, et al. Attention-Guided CNN for Image Denoising. Neural Networks, 2020, 124: 117-129. [30] ZHANG K, VAN GOOL L, TIMOFTE R.Deep Unfolding Network for Image Super-Resolution// Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2020: 3214-3223. [31] WANG H, XIE Q, ZHAO Q, et al. A Model-Driven Deep Neural Network for Single Image Rain Removal// Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2020: 3100-3109. [32] ZHANG Z H, LIU Y P, LIU J N, et al. AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing. IEEE Transactions on Image Processing, 2020, 30: 1487-1500. [33] ZHENG H Y, YONG H W, ZHANG L.Deep Convolutional Dictionary Learning for Image Denoising// Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2021: 630-641. [34] NOCI L, BACHMANN G, ROTH K, et al. Precise Characterization of the Prior Predictive Distribution of Deep ReLU Networks// Proc of the 35th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2021: 20851-20862. [35] ZHANG C N, BENZ P, ARGAW D M, et al. ResNet or Dense-Net? Introducing Dense Shortcuts to ResNet// Proc of the IEEE Winter Conference on Applications of Computer Vision. Washington, USA: IEEE, 2021: 3549-3558. [36] LIN Z, DUAN Z P, ZHANG Z, et al. FocusCut: Diving into a Focus View in Interactive Segmentation// Proc of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2022: 2627-2636. [37] ROTH S, BLACK M J. Fields of Experts// Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Re-cognition. Washington, USA: IEEE, 2005, III: 860-867. [38] MAIRAL J, BACH F, PONCE J, et al. Non-local Sparse Models for Image Restoration// Proc of the 12th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 2272-2279. [39] ZORAN D, WEISS Y.From Learning Models of Natural Image Patches to Whole Image Restoration// Proc of the International Conference on Computer Vision. Washington, USA: IEEE, 2011: 479-486. [40] BURGER H C, SCHULER C J, HARMELING S.Image Denoising: Can Plain Neural Networks Compete with BM3D?// Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2012: 2392-2399. [41] SCHMIDT U, ROTH S.Shrinkage Fields for Effective Image Restoration// Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 2774-2781. [42] CHEN Y J, POCK T.Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(6): 1256-1272. [43] ZHANG K, ZUO W M, GU S H, et al. Learning Deep CNN Denoiser Prior for Image Restoration// Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2017: 2808-2817.
2022, Vol. 35 
