Fast Correlation Computation Method for Matching Pursuit Algorithms in Compressed Sensing

TL;DR

This paper introduces a fast correlation computation method for matching pursuit algorithms in compressed sensing, significantly reducing computational complexity without sacrificing recovery performance when using certain sensing matrices.

Contribution

A novel fast correlation computation technique applicable to most MPAs with partial Fourier or Hadamard matrices, enhancing efficiency in compressed sensing.

Findings

Reduces computational complexity of MPAs substantially.

Applicable to almost all MPAs without performance loss.

Effective with partial Fourier and Hadamard sensing matrices.

Abstract

There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem a.k.a. compressed sensing (CS). In the MPAs, the correlation computation step has a dominant computational complexity. In this letter, we propose a new fast correlation computation method when we use some classes of partial unitary matrices as the sensing matrix. Those partial unitary matrices include partial Fourier matrices and partial Hadamard matrices which are popular sensing matrices. The proposed correlation computation method can be applied to almost all MPAs without causing any degradation of their recovery performance. And, for most practical parameters, the proposed method can reduce the computational complexity of the MPAs substantially.