Variational Denoising in Besov Spaces and Interpolation of Hard and Soft Wavelet Shrinkage

The relation of soft wavelet shrinkage (Donohoshrinkage) and variational denoising was discovered by Chambolle, Lucier et al. [3, 4]. Here we present an outline of this relation and give a non-convex generalization which will be related to hard wavelet shrinkage. This approach will lead to a “natural” interpolation between soft and hard shrinkage. AMS Subject Classification: 65K10, 42C40

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

[2]  I. Johnstone,et al.  Density estimation by wavelet thresholding , 1996 .

[3]  I. Johnstone,et al.  Minimax estimation via wavelet shrinkage , 1998 .

[4]  Antonin Chambolle,et al.  Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage , 1998, IEEE Trans. Image Process..

[5]  R. DeVore,et al.  Nonlinear approximation , 1998, Acta Numerica.

[6]  Hong-Ye Gao,et al.  Wavelet Shrinkage Denoising Using the Non-Negative Garrote , 1998 .

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

[8]  Antonin Chambolle,et al.  Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space , 2001, IEEE Trans. Image Process..

[9]  Mário A. T. Figueiredo,et al.  Wavelet-Based Image Estimation : An Empirical Bayes Approach Using Jeffreys ’ Noninformative Prior , 2001 .

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

[11]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[12]  Joachim Weickert,et al.  Correspondences between Wavelet Shrinkage and Nonlinear Diffusion , 2003, Scale-Space.

[13]  Alin Achim,et al.  SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling , 2003, IEEE Trans. Geosci. Remote. Sens..

[14]  K. Bredies,et al.  Mathematical concepts of multiscale smoothing , 2005 .