Matching Pursuits with Random Sequential Subdictionaries

TL;DR

This paper introduces a randomized approach to matching pursuits that reduces computational costs by using a sequence of subdictionaries, enabling efficient sparse approximation and signal compression.

Contribution

It proposes a novel non-adaptive random subdictionary selection method for matching pursuits, eliminating extra projection costs and parameter tuning.

Findings

Efficient sparse approximation with reduced computational complexity.

Theoretical modeling supports the probabilistic approach.

Successful application to audio signal compression.

Abstract

Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be computationally costly for large dictionaries and burdens their competitiveness in coding applications. We propose using a non adaptive random sequence of subdictionaries in the decomposition process, thus parsing a large dictionary in a probabilistic fashion with no additional projection cost nor parameter estimation. A theoretical modeling based on order statistics is provided, along with experimental evidence showing that the novel algorithm can be efficiently used on sparse approximation problems. An application to audio signal compression with multiscale time-frequency dictionaries is presented, along with a discussion of the complexity and practical implementations.