Nonlinear Harten's multiresolution on the quincunx pyramid

Authors:
Sergio Amat;S. Busquier;J. C. Trillo
Affiliations:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

Multiresolution transforms provide useful tools for image processing applications. For an optimal representation of the edges, it is crucial to develop nonlinear schemes which are not based on tensor product. This paper links the nonseparable quincunx pyramid and the nonlinear discrete Harten's multiresolution framework. In order to obtain the stability of these representations, an error-control multiresolution algorithm is introduced. A prescribed accuracy in various norms is ensured by these strategies. Explicit error bounds are presented. Finally, a nonlinear reconstruction is proposed and tested.