Cited By
View all- Yang ZYang YFan LBao B(2022)Truncated γ norm-based low-rank and sparse decompositionMultimedia Tools and Applications10.1007/s11042-022-12509-881:27(38279-38295)Online publication date: 1-Nov-2022
Image compressed sensing based on non-convex low-rank approximation
Authors: 
Yan Zhang, Jichang Guo, Chongyi LiAuthors Info & Claims
Pages 12853 - 12869
Abstract
Nonlocal sparsity and structured sparsity have been evidenced to improve the reconstruction of image details in various compressed sensing (CS) studies. The nonlocal processing is achieved by grouping similar patches of the image into the groups. To exploit these nonlocal self-similarities in natural images, a non-convex low-rank approximation is proposed to regularize the CS recovery in this paper. The nuclear norm minimization, as a convex relaxation of rank function minimization, ignores the prior knowledge of the matrix singular values. This greatly restricts its capability and flexibility in dealing with many practical problems. In order to make a better approximation of the rank function, the non-convex low-rank regularization namely weighted Schatten p-norm minimization (WSNM) is proposed. In this way, both the local sparsity and nonlocal sparsity are integrated into a recovery framework. The experimental results show that our method outperforms the state-of-the-art CS recovery algorithms not only in PSNR index, but also in local structure preservation.
References
[1]
Baraniuk RG, Cevher V, Duarte MF, Hegde C (2010) Model-based compressive sensing. IEEE Trans Inf Theory 56(4):1982---2001
[2]
Buades A, Coll B, Morel JM (2005) A review of image denoising algorithms, with a new one. Multiscale Modeling & Simulation 4(2):490---530
[3]
Cai JF, Candès EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956---1982
[4]
Candès EJ, Recht B (2009) Exact matrix completion via convex optimization. Found Comput Math 9(6):717---772
[5]
Candès EJ, Romberg J (2005) Practical signal recovery from random projections. Proc SPIE Comput Imag 5674:76---86
[6]
Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489---509
[7]
Candès EJ, Wakin MB, Boyd SP (2008) Enhancing sparsity by reweighted ℓ1 minimization. J Fourier Anal Appl 14(5---6):877---905
[8]
Candès EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis? J ACM 58(3):11
[9]
Chen SS, Donoho DL, Saunders MA (2001) Atomic decomposition by basis pursuit. SIAM Rev 43(1):129---159
[10]
Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080---2095
[11]
Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math 57(11):1413---1457
[12]
Dong W, Zhang L, Shi G (2011) Centralized sparse representation for image restoration. In 2011 International Conference on Computer Vision, pp 1259---1266
[13]
Dong W, Shi G, Li X, Zhang L, Wu X (2012) Image reconstruction with locally adaptive sparsity and nonlocal robust regularization. Signal Process Image Commun 27(10):1109---1122
[14]
Dong W, Shi G, Li X, Ma Y, Huang F (2014) Compressive sensing via nonlocal low-rank regularization. IEEE Trans Image Process 23(8):3618---3632
[15]
Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289---1306
[16]
Egiazarian K, Foi A, Katkovnik V (2007) Compressed sensing image reconstruction via recursive spatially adaptive filtering. In 2007 I.E. International Conference on Image Processing, 1, pp I-549---I-552
[17]
Foucart S, Lai MJ (2009) Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0<q?1. Appl Comput Harmon Anal 26(3):395---407
[18]
Gu S, Zhang L, Zuo W, Feng X (2014) Weighted nuclear norm minimization with application to image denoising. In 2014 I.E. Conference on Computer Vision and Pattern Recognition, pp 2862---2869
[19]
Huang J, Zhang T, Metaxas D (2011) Learning with structured sparsity. J Mach Learn Res 12:3371---3412
[20]
Jiang J, Ma X, Chen C, Lu T, Wang Z, Ma J (2017) Single image super-resolution via locally regularized anchored neighborhood regression and nonlocal means. IEEE Trans Multimedia 19(1):15---26
[21]
Lin Z, Chen M, Wu L, Ma Y (2009) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Dept. Electr. Comput. Eng., Univ. Illinois Urbana-Champaign, Urbana, IL, USA, Tech. Rep. UILU-ENG-09-2215
[22]
Liu R, Lin Z, De la Torre F, Su Z (2012, June) Fixed-rank representation for unsupervised visual learning. In 2012 I.E. Conference on Computer Vision and Pattern Recognition, pp 598---605
[23]
Liu L, Huang W, Chen DR (2014) Exact minimum rank approximation via Schatten p-norm minimization. J Comput Appl Math 267:218---227
[24]
Lu YM, Do MN (2008) Sampling signals from a union of subspaces. IEEE Signal Process Mag 25(2):41---47
[25]
Lu T, Xiong Z, Wan Y, Yang W (2016) Face hallucination via locality-constrained low-rank representation. In 2016 I.E. international conference on acoustics, speech and signal processing, pp. 1746-1750
[26]
Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Non-local sparse models for image restoration. In 2009 I.E. 12th International Conference on Computer Vision, pp 2272---2279
[27]
Massa A, Rocca P, Oliveri G (2015) Compressive sensing in electromagnetics-a review. IEEE Antennas and Propagation Magazine 57(1):224---238
[28]
Mirsky L (1975) A trace inequality of John von Neumann. Monatshefte für Mathematik 79(4):303---306
[29]
Natarajan BK (1995) Sparse approximate solutions to linear systems. SIAM J Comput 24(2):227---234
[30]
Nie F, Wang H, Cai X, Huang H, Ding C (2012, December) Robust matrix completion via joint schatten p-norm and lp-norm minimization. In 2012 I.E. 12th International Conference on Data Mining, pp 566---574
[31]
Pan JS, Li W, Yang CS, Yan LJ (2015) Image steganography based on subsampling and compressive sensing. Multimedia Tools and Applications 74(21):9191---9205
[32]
Sendur L, Selesnick IW (2002) Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans Signal Process 50(11):2744---2756
[33]
Software l1magic {Online} (2006) Available: http://www.acm.caltech.edu/l1magic
[34]
Tropp J, Gilbert AC (2005) Signal recovery from partial information via orthogonal matching pursuit
[35]
Wang Y, Wang J, Xu Z (2014) Restricted p-isometry properties of nonconvex block-sparse compressed sensing. Signal Process 104:188---196
[36]
Wang B, Lu T, Xiong Z (2016) Adaptive boosting for image denoising: Beyond low-rank representation and sparse coding. In 2016 International Conference on Pattern Recognition
[37]
Wipf DP, Rao BD (2004) Sparse Bayesian learning for basis selection. IEEE Trans Signal Process 52(8):2153---2164
[38]
Wu X, Dong W, Zhang X, Shi G (2012) Model-assisted adaptive recovery of compressed sensing with imaging applications. IEEE Trans Image Process 21(2):451---458
[39]
Xie Y, Gu S, Liu Y, Zuo W, Zhang W, Zhang L (2015) Weighted Schatten p-norm minimization for image Denoising and background subtraction. arXiv preprint arXiv:1512.01003
[40]
Xu BH, Cen YG, Wei Z, Cen Y, Zhao RZ, Miao ZJ (2016) Video restoration based on PatchMatch and reweighted low-rank matrix recovery. Multimedia Tools and Applications 75(5):2681---2696
[41]
Zhang D, Hu Y, Ye J, Li X, He X (2012) Matrix completion by truncated nuclear norm regularization. In 2012 I.E. Conference on Computer Vision and Pattern Recognition, pp 2192---2199
[42]
Zhang J, Xiang Q, Yin Y, Chen C, Luo X (2016) Adaptive compressed sensing for wireless image sensor networks. Multimedia Tools and Applications: 1---16
[43]
Zuo W, Meng D, Zhang L, Feng X, Zhang D (2013) A generalized iterated shrinkage algorithm for non-convex sparse coding. In Proceedings of the IEEE international conference on computer vision, pp 217---224
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Published: 01 May 2018
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View all- Yang ZYang YFan LBao B(2022)Truncated γ norm-based low-rank and sparse decompositionMultimedia Tools and Applications10.1007/s11042-022-12509-881:27(38279-38295)Online publication date: 1-Nov-2022
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