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.
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.
- Content Type Journal Article
- DOI 10.1007/s10915-009-9336-7
- Authors
- Sergio Amat, Universidad Politécnica de Cartagena Departamento de Matemática Aplicada y Estadística Cartagena Spain
- Juan Ruiz, Centro de Investigaciones Energéticas Medioambientales y Tecnológicas Madrid Spain
- J. Carlos Trillo, Universidad Politécnica de Cartagena Departamento de Matemática Aplicada y Estadística Cartagena Spain
- Journal Journal of Scientific Computing
- Online ISSN 1573-7691
- Print ISSN 0885-7474
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