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An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain

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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.

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References

  1. Antoniadis A, Fan J (2001) Regularization of wavelet approximations. J Am Stat Assoc 96(455):939–967

    Article  MathSciNet  MATH  Google Scholar 

  2. Blu T, Luisier F (2007) The SURE-LET approach to image denoising. IEEE Trans Image Process 16(11):2778–2786

    Article  MathSciNet  Google Scholar 

  3. 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

  4. Cai J-F, Cand’es EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982

    Article  MathSciNet  MATH  Google Scholar 

  5. 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

    Article  MathSciNet  MATH  Google Scholar 

  6. Chang S, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546

    Article  MathSciNet  MATH  Google Scholar 

  7. Chipman H, Kolaczyk E, McCulloc R (1997) Adaptive Bayesian wavelet shrinkage. J Am Stat Assoc 440(92):1413–1421

    Article  MATH  Google Scholar 

  8. Choi H, Baraniuk RG (2004) Multiple wavelet basis image denoising using Besov ball projections. IEEE Signal Process Lett 11(9):717–720

    Article  Google Scholar 

  9. 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

    Google Scholar 

  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

    Article  MathSciNet  Google Scholar 

  11. Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627

    Article  MathSciNet  MATH  Google Scholar 

  12. Donoho DL, Johnstone IM (1994) Ideal spatial adaptation via wavelet shrinkage. Biometrika 81:425–455

    Article  MathSciNet  MATH  Google Scholar 

  13. Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224

    Article  MathSciNet  MATH  Google Scholar 

  14. Gao HY (1998) Wavelet shrinkage denoising using the nonnegative garrote. J Comput Graph Stat 7(4):469–488

    Google Scholar 

  15. Gao HY, Bruce AG (1997) WaveShrink with firm shrinkage. Stat Sin 7:855–874

    MathSciNet  MATH  Google Scholar 

  16. Golub GH, Van Loan CF (1983) Matrix computations. John Hopkins University, Press, Baltimore

    MATH  Google Scholar 

  17. Gonzalez RC, Woods RE (2008) Digital image processing. Prentice-Hall, Upper Saddle River

    Google Scholar 

  18. Gu S, Zhang L, Zuo W, Feng X (2014) Weighted nuclear norm minimization with application to image denoising. IEEE Conf Comput Vis Pattern Recogn

  19. Hou Z (2003) Adaptive singular value decomposition in wavelet domain for image denoising. Pattern Recogn J Pattern Recogn Soc 36:1747–1763

    Article  MATH  Google Scholar 

  20. Jain P, Tyagi V (2013) Spatial and frequency domain filters for restoration of noisy images. IETE J Educ 54(2):108–116

    Article  Google Scholar 

  21. 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

  22. 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

    Article  Google Scholar 

  23. 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

    Article  MathSciNet  MATH  Google Scholar 

  24. 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

    Article  Google Scholar 

  25. Konstantinides K, Yao K (1988) Statistical analysis of effective singular values in matrix rank determination. IEEE Trans Acoust Speech Signal Process 757–763

  26. Luo G (2006) Fast wavelet image denoising based on local variance and edge analysis. Int J Intell Technol 1(2):165–175

    MathSciNet  Google Scholar 

  27. 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

    Article  MathSciNet  MATH  Google Scholar 

  28. Nason GP (1996) Wavelet shrinkage by cross-validation. J R Stat Soc B 58:463–479

    MATH  Google Scholar 

  29. 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

  30. 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

  31. Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Article  Google Scholar 

  32. 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

    Article  MathSciNet  MATH  Google Scholar 

  33. Pratt WK (2012) Digital image processing. Wiley, New York

    MATH  Google Scholar 

  34. 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

    Article  MathSciNet  MATH  Google Scholar 

  35. 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

    Article  Google Scholar 

  36. Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D 60:259–268

    Article  MathSciNet  MATH  Google Scholar 

  37. Sendur L, Selesnick IW (2002) Bivariate shrinkage with local variance estimation. IEEE Sig Process Lett 9(12):438–441

    Article  Google Scholar 

  38. 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

  39. Shapiro L, Stockman G (2001) Comput Vis. Prentice Hall

  40. 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

    MATH  Google Scholar 

  41. 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

  42. Van Der Veen AJ, Deprettere EF, Lee Swindlehurst A (1993) Subspace-based signal analysis using singular value decomposition. Proc IEEE 81:1277–1308

    Article  Google Scholar 

  43. Vidakovic B (1998) Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. J Am Stat Assoc 93(441):173–179

    Article  MathSciNet  MATH  Google Scholar 

  44. 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

    Article  Google Scholar 

  45. Weyrich N, Warhola GT (1998) Wavelet shrinkage and generalized cross validation for image denoising. IEEE Trans Image Process 7(1):82–90

    Article  Google Scholar 

  46. Wongsawat Y, Rao K, Oraintara S (2005) Multichannel SVD based image denoising. IEEE Int Symp Circuits syst 6:5990–5993

    Article  Google Scholar 

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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

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  • DOI: https://doi.org/10.1007/s11042-015-3154-8

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