Cooperative Greedy Pursuit Strategies for Sparse Signal Representation by Partitioning

TL;DR

This paper introduces cooperative greedy pursuit strategies for sparse signal approximation that partition signals and coordinate approximation steps to improve sparsity and quality, especially for music signals using redundant dictionaries.

Contribution

It proposes a novel cooperative approach combining forward and backward greedy steps for partitioned sparse approximation with redundant dictionaries.

Findings

Significant sparsity improvements over traditional methods.

Effective approximation of music signals with high quality.

Fast implementation enabled by FFT using redundant trigonometric dictionaries.

Abstract

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by producing high quality approximations of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transform.