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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

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00359740/en/
Date
2008
Journal name
Communications on Pure and Applied Mathematics
Volume
61
Number
9
Publisher
John Wiley & Sons
Pages
1173-1212
Publication identifier
http://dx.doi.org/10.1002/cpa.20242
Metadata
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Author(s)
Peyré, Gabriel
Mallat, Stéphane
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 / Keywords
Bandlets; image compression; orthogonal bandlets; geometric images

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    Mallat, Stéphane; Peyré, Gabriel (2007) Article accepté pour publication ou publié
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    Mallat, Stéphane; Peyré, Gabriel; Dossal, Charles; Le Pennec, Erwan (2007-09) Communication / Conférence
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