An Extension of the Interscale SURE-LET Approach for Image Denoising

In this paper, an extension of the interscale SURE-LET approach exploiting the interscale and intrascale dependencies of wavelet coefficients is proposed to improve denoising performance. This method incorporates information on neighbouring coefficients into the linear expansion of thresholds (LETs) without additional parameters to capture the texture characteristics of this image. The resulting interscale-intrascale wavelet estimator consists of a linear expansion of multivariate thresholding functions, whose parameters are optimized thanks to a multivariate Stein's unbiased risk estimate (SURE). Some experimental results are given to demonstrate the strength of the proposed method.

[1]  Jean-Michel Morel,et al.  Non-Local Means Denoising , 2011, Image Process. Line.

[2]  Peihua Qiu,et al.  Edge-preserving image denoising and estimation of discontinuous surfaces , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Amel Benazza-Benyahia,et al.  A Nonlinear Stein-Based Estimator for Multichannel Image Denoising , 2007, IEEE Transactions on Signal Processing.

[4]  B. Silverman,et al.  Incorporating Information on Neighboring Coefficients Into Wavelet Estimation , 2001 .

[5]  Mohamed-Jalal Fadili,et al.  A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior , 2006, Pattern Recognit. Lett..

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

[7]  Karen O. Egiazarian,et al.  Image denoising with block-matching and 3D filtering , 2006, Electronic Imaging.

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

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

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

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

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

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

[14]  Partha Sarathi Mukherjee,et al.  Edge structure preserving image denoising , 2010, Signal Process..

[15]  Thierry Blu,et al.  The SURE-LET Approach to Image Denoising , 2007, IEEE Transactions on Image Processing.

[16]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.

[17]  Michael J. Black,et al.  Fields of Experts: a framework for learning image priors , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[18]  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.

[19]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[20]  Robert D. Nowak,et al.  Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior , 2001, IEEE Trans. Image Process..

[21]  Mohamed-Jalal Fadili,et al.  Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities , 2005, IEEE Transactions on Image Processing.

[22]  Thierry Blu,et al.  A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding , 2007, IEEE Transactions on Image Processing.

[23]  I. Selesnick,et al.  Bivariate shrinkage with local variance estimation , 2002, IEEE Signal Processing Letters.

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

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

[26]  Yacov Hel-Or,et al.  A Discriminative Approach for Wavelet Denoising , 2008, IEEE Transactions on Image Processing.

[27]  C. Stein.  Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

[28]  Thierry Blu,et al.  SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding , 2008, IEEE Transactions on Image Processing.