Abstract
Image denoising has always been one of the standard problems in image processing and computer vision. It is always recommendable for a denoising method to preserve important image features, such as edges, corners, etc., during its execution. Image denoising methods based on wavelet transforms have been shown their excellence in providing an efficient edge-preserving image denoising, because they provide a suitable basis for separating noisy signal from the image signal. This paper presents a novel edge-preserving image denoising technique based on wavelet transforms. The wavelet domain representation of the noisy image is obtained through its multi-level decomposition into wavelet coefficients by applying a discrete wavelet transform. A patch-based weighted-SVD filtering technique is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method achieves very impressive gain in denoising performance.
Similar content being viewed by others
References
Antoniadis A, Fan J (2001) Regularization of wavelet approximations. J Am Stat Assoc 96(455):939–967
Blu T, Luisier F (2007) The SURE-LET approach to image denoising. IEEE Trans Image Process 16(11):2778–2786
Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In Proceeding of IEEE International Conference on Computer Vision and Pattern Recognition, vol. 2. San Diego, CA, USA: IEEE Press, pp. 60–65
Cai J-F, Cand’es EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982
Chang S, Yu B, Vetterli M (2000) Spatially adaptive wavelet thresholding based on context modeling for image denoising. IEEE Trans Image Process 9(9):1522–1531
Chang S, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546
Chipman H, Kolaczyk E, McCulloc R (1997) Adaptive Bayesian wavelet shrinkage. J Am Stat Assoc 440(92):1413–1421
Choi H, Baraniuk RG (2004) Multiple wavelet basis image denoising using Besov ball projections. IEEE Signal Process Lett 11(9):717–720
Dabov K, Foi A, Katkovnik V, Egiazarian K (2006) Image denoising with block-matching and 3D filtering. SPIE Electron Imaging Algorithm Syst 6064:606414–1–606414–12
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
Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627
Donoho DL, Johnstone IM (1994) Ideal spatial adaptation via wavelet shrinkage. Biometrika 81:425–455
Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224
Gao HY (1998) Wavelet shrinkage denoising using the nonnegative garrote. J Comput Graph Stat 7(4):469–488
Gao HY, Bruce AG (1997) WaveShrink with firm shrinkage. Stat Sin 7:855–874
Golub GH, Van Loan CF (1983) Matrix computations. John Hopkins University, Press, Baltimore
Gonzalez RC, Woods RE (2008) Digital image processing. Prentice-Hall, Upper Saddle River
Gu S, Zhang L, Zuo W, Feng X (2014) Weighted nuclear norm minimization with application to image denoising. IEEE Conf Comput Vis Pattern Recogn
Hou Z (2003) Adaptive singular value decomposition in wavelet domain for image denoising. Pattern Recogn J Pattern Recogn Soc 36:1747–1763
Jain P, Tyagi V (2013) Spatial and frequency domain filters for restoration of noisy images. IETE J Educ 54(2):108–116
Jain P, Tyagi V (2014) A survey of edge-preserving image denoising methods. Inf Syst Front 1–12. doi: 10.1007/s10796-014-9527-0
Jain P, Tyagi V (2015) An adaptive edge-preserving image denoising technique using tetrolet transforms. Vis Comput 31(5):657–674. doi:10.1007/s00371-014-0993-7
Jain P, Tyagi V (2015) LAPB: locally adaptive patch-based wavelet domain edge-preserving image denoising. Inform Sci 294:164–181. doi:10.1016/j.ins.2014.09.060
Konstantinides K, Natarajan B, Yovanof GS (1997) Noise estimation and filtering using block-based singular value decomposition. IEEE Trans Image Process 6(3):479–483
Konstantinides K, Yao K (1988) Statistical analysis of effective singular values in matrix rank determination. IEEE Trans Acoust Speech Signal Process 757–763
Luo G (2006) Fast wavelet image denoising based on local variance and edge analysis. Int J Intell Technol 1(2):165–175
Maggioni M, Katkovnik V, Egiazarian K, Foi A (2013) Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Trans Image Process 22(1):119–133
Nason GP (1996) Wavelet shrinkage by cross-validation. J R Stat Soc B 58:463–479
Nason GP, Silverman BW (1995) The stationary wavelet transform and some statistical applications. In: Lecture notes in statistics: wavelets and statistics, Springer-Verlag, Berlin, pp. 281–300
Orchard J, Ebrahimi M, Wong A (2008) Efficient nonlocal-means denoising using the SVD. In: IEEE international conference on image processing. San Diego, CA, USA 1732–1735
Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639
Portilla J, Strela V, Wainwright M, Simoncelli E (2003) Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans Image Process 12(11):1338–1351
Pratt WK (2012) Digital image processing. Wiley, New York
Qiu T, Wang A, Yu N, Song A (2013) LLSURE: local linear sure-based edge-preserving image filtering. IEEE Trans Image Process 22(1):80–90
Rudin L, Osher S (1994) Total variation based image restoration with free local constraints. Proc IEEE Int Conf Image Process 1:31–35, Austin, Texas, USA
Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D 60:259–268
Sendur L, Selesnick IW (2002) Bivariate shrinkage with local variance estimation. IEEE Sig Process Lett 9(12):438–441
Shao L, Yan R, Li X, Liu Y. From heuristic optimization to dictionary learning: a review and comprehensive comparison of image denoising algorithms 1–14
Shapiro L, Stockman G (2001) Comput Vis. Prentice Hall
Silva RD, Minetto R, Schwartz WR, Pedrini H (2012) Adaptive edge-preserving image denoising using wavelet transforms. Pattern Anal Appl. doi:10.1007/s10044-012-0266-x, Springer-Verlag
Tomasi C, Manduchi R (1998) Bilateral filtering for gray and color images. In proceeding of 6th International Conference on Computer Vision., Bombay, India 839–846
Van Der Veen AJ, Deprettere EF, Lee Swindlehurst A (1993) Subspace-based signal analysis using singular value decomposition. Proc IEEE 81:1277–1308
Vidakovic B (1998) Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. J Am Stat Assoc 93(441):173–179
Wang Z, Bovik A, Sheikh H, Simoncelli E (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612
Weyrich N, Warhola GT (1998) Wavelet shrinkage and generalized cross validation for image denoising. IEEE Trans Image Process 7(1):82–90
Wongsawat Y, Rao K, Oraintara S (2005) Multichannel SVD based image denoising. IEEE Int Symp Circuits syst 6:5990–5993
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jain, P., Tyagi, V. An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain. Multimed Tools Appl 76, 1659–1679 (2017). https://doi.org/10.1007/s11042-015-3154-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-015-3154-8