Optimal tree approximation with wavelets

The more a;priori knowledge we encode into a signal processing algorithm, the better performance we can expect. In this paper, we overview several approaches to capturing the structure of singularities ledges, ridges, etc.) in wavelet-based signal processing schemes. Leveraging results from-approximation theory, we discuss nonlinear approximations on trees and point out that an optimal tree approximant exists and is easily computed. The optimal tree approximation inspires a new hierarchical interpretation of the wavelet decomposition and a tree-based wavelet denoising algorithm that suppresses spurious noise bumps.