Convex multiresolution analysis
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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:
Pattern Analysis and Machine Intelligence, IEEE Transactions on
(Volume:20
,
Issue:
12
)
Date of Publication: Dec 1998