Convex multiresolution analysis

Author

Combettes, Patrick L. ; Pesquet, Jean-Christophe

Author_Institution

Dept. of Electr. Eng., City Univ. of New York, NY, USA

Volume

20

Issue

12

fYear

1998

fDate

12/1/1998 12:00:00 AM

Firstpage

1308

Lastpage

1318

Abstract

A standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties. We propose a nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets. These sets are chosen so as to provide a recursive, monotone approximation scheme that allows for various signal and image features to be investigated. Several classes of convex multiresolution analyses are discussed and numerical applications to signal and image-processing problems are demonstrated

Keywords

Hilbert spaces; approximation theory; filtering theory; image processing; set theory; wavelet transforms; Hilbert space; approximation; convex sets; hierarchical signal processing; image-processing; monotone sequence; multiresolution analysis; nonlinear filter banks; projections; vector subspaces; wavelet analysis; Helium; Hilbert space; Image analysis; Image processing; Multiresolution analysis; Nonlinear filters; Signal analysis; Signal processing; Signal resolution; Wavelet analysis;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.735804

Filename

735804