Abstract
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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Research of S. Amat was supported in part by the Spanish grants MTM2007-62945 and 08662/PI/08.
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Amat, S., Ruiz, J. & Trillo, J.C. Fast Multiresolution Algorithms and Their Related Variational Problems for Image Denoising. J Sci Comput 43, 1–23 (2010). https://doi.org/10.1007/s10915-009-9336-7
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DOI: https://doi.org/10.1007/s10915-009-9336-7