Abstract
In recent years, compressive sensing has been one promising technique for denoising images. This paper presents a new denoising model based on blocking sparsity. First, an image is blocked. Second, the split-Bregman method is used to solve for each block image. Finally, all denoised block images are combined into one image. Compared with the latest HTV, GHNS, FastATV, CSR and BM3D models, experimental results demonstrate that the proposed method is efficient, and has better denoising capability.
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References
Ji Z, Chen Q, Sun Q, Xia DS (2009) A moment-based nonlocal-means algorithm for image denoising. Inf Process Lett 109:1238–1244
Oh S, Woo H, Yun S, Kang M (2013) Non-convex hybrid total variation for image denoising. J Vis Commun Image Represent 24:332–344
Atlas A, Karami F, Meskine D (2014) The Perona–Malik inequality and application to image denoising. Nonlinear Anal Real World Appl 18:57–68
Liu X, Huang L (2014) A new nonlocal total variation regularization algorithm for image denoising. Math Comput Simul 97:224–233
Tracey BH, Miller EL, Wu Y, Natarajan P, Noonan JP (2014) A constrained optimization approach to combining multiple non-local means denoising estimates. Signal Process 103:60–68
SuryaPrasath VB, Vorotnikov D (2014) Weighted and well-balanced anisotropic diffusion scheme for image denoising and restoration. Nonlinear Anal Real World Appl 17:33–46
Manjn JV, Coup P, Buades A (2015) MRI noise estimation and denoising using non-local PCA. Med Image Anal 22:35–47
Fu B, Li W, Fu YP, Song CM (2015) An image topic model for image denoising. Neurocomputing 169:119–123
Chen F, Zeng X, Wang M (2015) Image denoising via local and nonlocal circulant similarity. J Vis Commun Image Represent 30:117–124
Jiang J, Yang J, Cui Y, Wong W, Lai Z (2015) Sparse nonlocal priors based two-phase approach for mixed noise removal. Sig Process 116:101–111
Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60(1–4):259–268
Lysaker M, Lundervold A, Tai XC (2003) Noise removal using fourth-order partial differential equation with application to medical magnetic resonance images in space and time. IEEE Trans Image Process 12(12):1579–1590
Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639
Arian M, Manjari N, Richard B (2013) Anisotropic nonlocal means denoising. Appl Comput Harmon Anal 35:452–482
Wang Y, Ren W, Wang H (2013) Anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising. Comput Math Appl 66:1729–1742
Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546
Somnath M, Mandal JK (2013) Wavelet based denoising of medical images using sub-band adaptive thresholding through genetic algorithm. Proc Technol 10:680–689
Elad M (2002) On the origin of the bilateral filter and ways to improve it. IEEE Trans Image Process 11:1141–1151
Yang HY, Wang XY, Qu TX, Fu ZK (2011) Image denoising using bilateral filter and Gaussian scale mixtures in shiftable complex directional pyramid domain. Comput Electr Eng 37(5):656–668
Buades A, Coll B, Morel J (2005) A non-local algorithm for image denoising. In: Proceedings of IEEE international conference on computer vision
Hu J, Luo YP (2013) Non-local means algorithm with adaptive patch size and bandwidth. Optik 124:5639–5645
Yang M, Liang J, Zhang J, Gao H, Meng F, Li X, Song S (2013) Non-local means theory based Perona–Malik model for image denosing. Neurocomputing 120:262–267
Luo H, Wang Y (2016) Sparse regularization image denoising based on gradient histogram and non-local self-similarity in WMSN. Optik 127:1743–1747
Tang Y, Chen Y, Xu N, Jiang A, Zhou L (2016) Image denoising via sparse coding using eigenvectors of graph Laplacian. Digit Signal Proc 50:114–122
Nejati M, Samavi S, Derksen H, Najarian K (2016) Denoising by low-rank and sparse representations. J Vis Commun Image Represent 36:28–39
Majumdar A, Ansari N, Aggarwal H, Biyani P (2016) Impulse denoising for hyper-spectral images: a blind compressed sensing approach. Sig Process 119:136–141
Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095
Dong W, Li X, Zhang L, Shi G (2011) Sparsity-based image denoising via dictionary learning and structural clustering. Comput Vis Pattern Recognit (CVPR) 2011:457–464
Li F, Shen C, Fan J, Shen C (2007) Image restoration combining a total variational filter and a fourth-order filter. J Vis Commun Image Represent 18(4):322–330
Goldstein T, Osher S (2009) The split Bregman method for \(L_1\)-regularized problems. SIAM J Imaging Sci 2(2):323–343
Jia R, Zhao H (2010) A fast algorithm for the total variation model of image denoising. Adv Comput Math 33(2):231–241
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:600–612
Zhang L, Zhang L, Mou X, Zhang D (2011) FSIM: a feature similarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386
Chao SM, Tsai DM (2010) An improved anisotropic diffusion model for detail and edge preserving smoothing. Pattern Recogn Lett 31:2012–2023
Tebini S, Mbarki Z, Seddik H, BenBraiek E (2016) Rapid and efficient image restoration technique based on new adaptive anisotropic diffusion function. Digit Signal Proc 48:201–215
Acknowledgements
I appreciates my graduate student, Jiao He. She makes some contributions for the revision of the manuscript. This work is supported by Fundamental Research Funds for the Central Universities (No. XDJK2020B033).
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Yuan, J., He, J. Blocking sparse method for image denoising. Pattern Anal Applic 24, 1125–1133 (2021). https://doi.org/10.1007/s10044-021-00974-0
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DOI: https://doi.org/10.1007/s10044-021-00974-0