Orthogonal Bandlet Bases for Geometric Images Approximation
Peyré, Gabriel; Mallat, Stéphane (2008), Orthogonal Bandlet Bases for Geometric Images Approximation, Communications on Pure and Applied Mathematics, 61, 9, p. 1173-1212. http://dx.doi.org/10.1002/cpa.20242
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00359740/en/
Journal nameCommunications on Pure and Applied Mathematics
John Wiley & Sons
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Abstract (EN)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.
Subjects / KeywordsBandlets; image compression; orthogonal bandlets; geometric images
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