An exact tree projection algorithm for wavelets

TL;DR

This paper introduces an exact dynamic programming algorithm for projecting signals onto wavelet tree structures, ensuring precise results with proven computational complexity.

Contribution

It presents the first guaranteed exact projection algorithm for wavelet trees, improving upon approximate methods.

Findings

Algorithm guarantees exact projection onto wavelet trees.

Proven complexity of O(Nk) for the algorithm.

Applicable to sparse signal approximation in wavelet domains.

Abstract

We propose a dynamic programming algorithm for projection onto wavelet tree structures. In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to calculate the projection exactly. We also prove that our algorithm has O(Nk) complexity, where N is the signal dimension and k is the sparsity of the tree approximation.