Convex multiresolution analysis

A standard wavelet multiresolution analysis can be defined via a sequence of projection operators onto a monotone sequence of closed vector subspaces possessing suitable invariance properties. We propose an extension of this framework in which the linear projection operators are replaced by nonlinear retractions onto convex sets. These retractions are chosen so as to provide a recursive, monotone signal approximation scheme. Numerical simulations are also provided.

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