Nonlinear thresholding of multiresolution decompositions adapted to the presence of discontinuities

Authors:
Sergio Amat;Jacques Liandrat
Affiliations:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain;Centrale Marseille, LATP, Marseille, France 13451
Venue:
Advances in Computational Mathematics
Year:
2013

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Abstract

A new nonlinear representation of multiresolution decompositions and new thresholding adapted to the presence of discontinuities are presented and analyzed. They are based on a nonlinear modification of the multiresolution details coming from an initial (linear or nonlinear) scheme and on a data dependent thresholding. Stability results are derived. Numerical advantages are demonstrated on various numerical experiments.