When considering fast multiresolution techniques for image denoising problems, there are three important aspects. The first one is the choice of the specific multiresolution, the second one the choice of a proper filt...
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When considering fast multiresolution techniques for image denoising problems, there are three important aspects. The first one is the choice of the specific multiresolution, the second one the choice of a proper filter function and the third one the choice of the thresholding parameter. Starting from the classical one, namely, linear wavelet algorithms with Donoho and Johnstone's Soft-thresholding with the universal shrinkage parameter, the first aim of this paper is to improve it in the three mentioned directions. Thus, a new nonlinear approach is proposed and analyzed. On the other hand, the linear approach of Donoho and Johnstone is related with a well known variational problem. Our second aim is to find a related variational problem, more adapted to the denoising problem, for the new approach. We would like to mention that the analysis of theoretical properties in a nonlinear setting are usually notoriously more difficult. Finally, a comparison with other approaches, including linear and nonlinear multiresolution schemes, SVD-based schemes and filters with a non-multiresolution nature, is presented.
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