A New Fuzzy-Based Wavelet Shrinkage Image Denoising Technique

This paper focuses on fuzzy image denoising techniques. In particular, we investigate the usage of fuzzy set theory in the domain of image enhancement using wavelet thresholding. We propose a simple but efficient new fuzzy wavelet shrinkage method, which can be seen as a fuzzy variant of a recently published probabilistic shrinkage method [1] for reducing adaptive Gaussian noise from digital greyscale images. Experimental results show that the proposed method can efficiently and rapidly remove additive Gaussian noise from digital greyscale images. Numerical and visual observations show that the performance of the proposed method outperforms current fuzzy non-wavelet methods and is comparable with some recent but more complex wavelets methods. We also illustrate the main differences between this version and the probabilistic version and show the main improvements in comparison to it.

[1]  H. L. Resnikoff,et al.  Wavelet analysis: the scalable structure of information , 1998 .

[2]  Xiang-Gen Xia,et al.  Improved hidden Markov models in the wavelet-domain , 2001, IEEE Trans. Signal Process..

[3]  Ivan Kalaykov,et al.  Fuzzy-Similarity-Based Image Noise Cancellation , 2002, AFSS.

[4]  Dimitri Van De Ville,et al.  Noise reduction by fuzzy image filtering , 2003, IEEE Trans. Fuzzy Syst..

[5]  Aleksandra Pizurica,et al.  Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising , 2006, IEEE Transactions on Image Processing.

[6]  Edward H. Adelson,et al.  Noise removal via Bayesian wavelet coring , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[7]  Aleksandra Pizurica,et al.  A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising , 2002, IEEE Trans. Image Process..

[8]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[9]  Michio Sugeno,et al.  Advances in Soft Computing — AFSS 2002 , 2002, Lecture Notes in Computer Science.

[10]  Justin K. Romberg,et al.  Bayesian tree-structured image modeling using wavelet-domain hidden Markov models , 2001, IEEE Trans. Image Process..

[11]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

[12]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[13]  Etienne E. Kerre,et al.  Fuzzy random impulse noise reduction method , 2007, Fuzzy Sets Syst..

[14]  Pao-Ta Yu,et al.  Weighted fuzzy mean filters for image processing , 1997, Fuzzy Sets Syst..

[15]  Yau-Hwang Kuo,et al.  High-stability AWFM filter for signal restoration and its hardware design , 2000, Fuzzy Sets Syst..

[16]  Yuan F. Zheng,et al.  Feature-based wavelet shrinkage algorithm for image denoising , 2005, IEEE Transactions on Image Processing.

[17]  Hon Keung Kwan,et al.  Fuzzy filters for image filtering , 2002, The 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002..

[18]  H. Chipman,et al.  Adaptive Bayesian Wavelet Shrinkage , 1997 .

[19]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[20]  Kannan Ramchandran,et al.  Low-complexity image denoising based on statistical modeling of wavelet coefficients , 1999, IEEE Signal Processing Letters.

[21]  Dirk Roose,et al.  Wavelet-based image denoising using a Markov random field a priori model , 1997, IEEE Trans. Image Process..

[22]  P. H. Lindsay.  Human Information Processing , 1977 .

[23]  Levent Sendur,et al.  Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency , 2002, IEEE Trans. Signal Process..

[24]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[25]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[26]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[27]  Jung-Hua Wang,et al.  HAF: an Adaptive Fuzzy Filter for Restoring Highly Corrupted Images by Histogram Estimation , 1999 .

[28]  Fuyuan Peng,et al.  Adaptive fuzzy switching filter for images corrupted by impulse noise , 2004, ICCCAS 2004.

[29]  Bin Yu,et al.  Wavelet thresholding via MDL for natural images , 2000, IEEE Trans. Inf. Theory.

[30]  Adhemar Bultheel,et al.  Empirical Bayes Approach to Improve Wavelet Thresholding for Image Noise Reduction , 2001 .

[31]  X. Xia,et al.  Image denoising using a local contextual hidden Markov model in the wavelet domain , 2001, IEEE Signal Process. Lett..

[32]  Lotfi A. Zadeh,et al.  Fuzzy Logic and Its Application to Approximate Reasoning , 1974, IFIP Congress.

[33]  Guoliang Fan,et al.  Image denoising using a local contextual hidden Markov model in the wavelet domain , 2001, IEEE Signal Processing Letters.

[34]  Ivan Kalaykov,et al.  Fuzzy-similarity-based noise cancellation for real-time image processing , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[35]  Etienne Kerre,et al.  Fuzzy Impulse Noise Reduction Methods for Color Images , 2006 .

[36]  Eero P. Simoncelli,et al.  Image Denoising using Gaussian Scale Mixtures in the Wavelet Domain , 2002 .

[37]  B. Vidakovic.  Nonlinear wavelet shrinkage with Bayes rules and Bayes factors , 1998 .

[38]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..