Abstract
Image denoising is a widely used approach in the field of image processing, which restores image more accurately. In particular, higher-order singular value decomposition (HOSVD) algorithm is a prominent algorithm for image denoising. However, traditional HOSVD transform utilizes the fixed threshold to truncate the small transform coefficients under the condition of a given tensor. Thus, some intrinsic properties of the tensor are ignored. In this paper, we propose an adaptive thresholding HOSVD with rearrangement of tensors, called ATH-HOSVD. First, the tensor-based HOSVD transform is employed to exploit the nonlocal tensor property. Second, we consider the spatial distribution of elements in the core tensors and adopt the indices of transform coefficients to produce adaptive threshold. Finally, in order to improve the sparsity of tensors, a rearrangement of tensors based on the amplitude sorting and Hilbert space-filling curve is integrated into the scheme of adaptive thresholding HOSVD. Various experiments on natural images are reported to not only demonstrate the effectiveness of the proposed ATH-HOSVD method, but also show its competitive speed.
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References
Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing Overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322
Azzari L, Foi A (2016) Variance stabilization for noisy+estimate combination in iterative Poisson denoising. IEEE Signal Process Lett 23(8):1086–1090
Beck A, Teboulle M (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans Image Process 18(11):2419
Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. in: IEEE Comput Soc Conf Comput Vis Pattern Recogn 2:60–65
Chambolle A (2004) An algorithm for Total variation minimization and applications. Kluwer Academic Publishers
Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532
Cristovao C, Alessandro F, Vladimir K, et al (2018) Nonlocality-reinforced convolutional neural networks for image denoising. IEEE Signal Proces Lett 1-1
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
Dong W, Zhang L, Shi G (2013) Centralized sparse representation for image restoration. IEEE Trans Image Process 22(4):1620–1630
Dong W, Shi G, Li X (2013) Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans Image Process 22(2):700–711
Dong W, Shi G, Li X et al (2014) Compressive sensing via nonlocal low-rank regularization. IEEE Transact Image Process A Publ IEEE Signal Process Soc 23(8):3618
Donoho DL (1992) Denoising via soft thresholding. IEEE Trans Inf Theory
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745
Elmoataz A, Lezoray O, Bougleux S (2008) Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Press
Eslahi N, Aghagolzadeh A (2016) Compressive sensing image restoration using adaptive Curvelet Thresholding and nonlocal sparse regularization. IEEE Trans Image Process 25(7):3126–3140
Feng L, Sun H, Sun Q et al (2016) Compressive sensing via nonlocal low-rank tensor regularization. Neurocomputing 216(C):45–60
Fu Y, Dong W (2016) 3D magnetic resonance image denoising using low-rank tensor approximation. Neurocomputing 195:30–39
Gu S, Zhang L, Zuo W, Feng X (2014) Weighted nuclear norm minimization with application to image Denoising. IEEE Conference on Computer Vision and Pattern Recognition 2862-2869
He L, Carin L (2009) Exploiting structure in wavelet-based Bayesian compressive sensing. IEEE Trans Signal Process 57(9):3488–3497
He N, Wang JB, Zhang LL et al (2016) Non-local sparse regularization model with application to image denoising. Multimed Tools Appl 75(5):2579–2594
vHu H, Froment J, Liu Q (2015) Patch-based low-rank minimization for image denoising. Computer Science. 50
Lai Z, Qu X, Liu Y et al (2015) Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform. Med Image Anal 27:93
Liu H, Xiong R, Zhang J, et al (2015) Image denoising via adaptive soft-thresholding based on non-local samples. Computer Vision and Pattern Recognition. IEEE:484–492
Liu S, Cao J, Liu H, et al (2017) MRI reconstruction via enhanced group sparsity and nonconvex regularization. Neurocomputing 272
Luisier F, Blu T, Unser M (2011) Image Denoising in mixed Poisson–Gaussian noise. IEEE Press
Mairal J, Bach F, Ponce J et al (2010) Non-local sparse models for image restoration. IEEE, Int Conf Comput Vis 30:2272–2279
Mäkitalo M, Foi A (2013) Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise. IEEE Trans Image Process 22(1):91–103
Moon B, Jagadish HV, Faloutsos C et al (2001) Analysis of the clustering properties of the Hilbert space-filling curve. Knowledge Data Eng IEEE Transact 13(1):124–141
Peng Y, Meng D, Xu Z, et al (2014) Decomposable nonlocal tensor dictionary learning for multispectral image Denoising. Computer Vision and Pattern Recognition IEEE:2949–2956
Pérez-Demydenko C, Brito-Reyes I, Fernández BA et al (2014) The complete set of homogeneous Hilbert curves in two dimensions. Appl Math Comput 234(C):531–542
Peyré G (2008) Image processing with nonlocal spectral bases. Siam J Multiscale Model Simul 7(2):703–730
Rajwade A, Rangarajan A, Banerjee A (2013) Image Denoising using the higher order singular value decomposition. IEEE Transact Pattern Analysis Mach Intell 35(4):849–862
Remenyi N, Nicolis O, Nason G, Vidakovic B (2014) Image Denoising with 2D scale-mixing complex wavelet transforms. IEEE Trans Image Process 23(12):5165–5174
Rezghi M (2017) A novel fast tensor-based Preconditioner for image restoration. IEEE Trans Image Process PP(99):1
Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1–4):259–268
Starck JL, Candes EJ, Donoho DL (2002) The Curvelet transform for image Denoising. IEEE Trans Image Process 11(6):670–684
Tai Y, Yang J, Liu X and Xu C (2017) MemNet: a persistent memory network for image restoration. IEEE International Conference on Computer Vision (ICCV), pp. 4549-4557.
Wang Q, Zhang X, Wu Y, et al (2017) Non-convex weighted lp minimization based group sparse representation framework for image denoising. IEEE Signal Process Lett PP(99):1
Wang X., Girshick R., Gupta A., He K. (2018) Non-local neural networks. Comput Vis Patt Recogn (CVPR)
Zhang M, Gunturk BK (2008) Multiresolution bilateral filtering for image denoising. IEEE Transact Image Process A Publ IEEE Signal Process Soc 17(12):2324–2333
Zhang X, Burger M, Bresson X et al (2010) Bregmanized nonlocal regularization for Deconvolution and sparse reconstruction. Siam J Imaging Sci 3(3):253–276
Zhang L, Dong W, Zhang D et al (2010) Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recogn 43(4):1531–1549
Zhang J, Zhao D, Zhao C et al (2012) Compressed sensing recovery via collaborative Sparsity. Data Compress Conf IEEE 5:287–296
Zhang J, Xiong R, Chen Z, et al (2012) Exploiting image local and nonlocal consistency for mixed Gaussian-impulse noise removal. IEEE Int Conf on Multimed Expo. IEEE:592-597
Zhang K, Gao X, Tao D, Li X (2012) Single image super-resolution with non-local means and steering kernel regression. IEEE Trans Image Process 21(11):4544–4556
Zhang J, Zhao D, Xiong R et al (2014) Image restoration using joint statistical modeling in a space-transform domain. IEEE Transact Circ Syst Vid Technol 24(6):915–928
Zhang J, Zhao C, Zhao D et al (2014) Image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization. Signal Process 103(10):114–126
Zhang J, Zhao D, Gao W (2014) Group-based sparse representation for image restoration. IEEE Transact Image Process A Publ IEEE Signal Process Soc 23(8):3336–3351
Zoran D, Weiss Y (2011) From learning models of natural image patches to whole image restoration. 6669(5):479-486
Acknowledgements
This work is supported in part by the National Science Foundation of China (Grant No. U1903213), the Science and Technology Program of Xi’an Municipality (Grant No. GXYD11.1) and the Zhejiang Provincial National Science Foundation of China (Grant No. LQY19F010001).
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Li, Y., Pan, Z., Du, D. et al. Adaptive thresholding HOSVD with rearrangement of tensors for image denoising. Multimed Tools Appl 79, 19575–19593 (2020). https://doi.org/10.1007/s11042-020-08624-z
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DOI: https://doi.org/10.1007/s11042-020-08624-z