Premium
On some new variational problems for image denoising
Author(s) -
Amat Sergio,
Busquier Sonia,
Ruiz Juan,
Trillo Juan Carlos,
Zouaoui Sofiane
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5783
Subject(s) - mathematics , discretization , noise reduction , image denoising , nonlinear system , mathematical optimization , image (mathematics) , multiresolution analysis , wavelet , algorithm , artificial intelligence , mathematical analysis , computer science , wavelet transform , physics , quantum mechanics , discrete wavelet transform
This paper is devoted to image denoising problems using multiresolution schemes related to variational problems. We start with the linear approach of Donoho and Johnstone, that is related to a well known diffusion‐type variational problem. In order to improve the behavior of this approach, we propose some new nonlinear variational problems more adapted to the problem of denoising. Moreover, the discretization is performed using nonlinear multiresolution schemes. In particular, we obtain some fast and well adapted schemes for the considered problem of denoising.