Nonlinear multiresolution image analysis via convex projections

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 image features to be investigated. Several classes of convex multiresolution analyzes are discussed and numerical applications to image analysis are demonstrated