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Convex multiresolution analysis

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2 Author(s)
P. L. Combettes ; Dept. of Electr. Eng., City Univ. of New York, NY, USA ; J. -C. Pesquet

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

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:20 ,  Issue: 12 )