A Projection Operator for the Restoration of Divergence-Free Vector Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational methods in image segmentation
Variational methods in image segmentation
Scale-Space From Nonlinear Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Nonlinear Decomposition: The Sieve Decomposition Theorem
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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.