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Journal Articles Communications on Pure and Applied Mathematics Year : 2008

Orthogonal Bandlet Bases for Geometric Images Approximation

Abstract

This paper introduces orthogonal bandelet bases to approximate images having some geometrical regularity. These bandelet bases are computed by applying parametrized Alpert transform operators over an orthogonal wavelet basis. These bandeletization operators depend upon a multiscale geometric flow that is adapted to the image at each wavelet scale. This bandelet construction has a hierarchical structure over wavelet coefficients taking advantage of existing regularity among these coefficients. It is proved that C˛ -images having singularities along Calpha-curves are approximated in a best orthogonal bandelet basis with an optimal asymptotic error decay. Fast algorithms and compression applications are described.
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Dates and versions

hal-00359740 , version 1 (09-02-2009)

Identifiers

  • HAL Id : hal-00359740 , version 1

Cite

Stéphane Mallat, Gabriel Peyré. Orthogonal Bandlet Bases for Geometric Images Approximation. Communications on Pure and Applied Mathematics, 2008, 61 (9), pp.1173-1212. ⟨hal-00359740⟩
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