New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit

TL;DR

This paper introduces a new coherence measure called global 2-coherence, linking it to existing metrics to improve theoretical bounds for sparse signal recovery using greedy algorithms like OMP in compressive sensing.

Contribution

It defines the global 2-coherence, explores its relationship with mutual coherence and RIP, and derives improved bounds for sparse recovery success.

Findings

Established a new coherence index, the global 2-coherence.

Derived relationships between global 2-coherence, mutual coherence, and RIP.

Provided improved bounds for OMP success in sparse recovery.

Abstract

In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we obtain more general results on sparse signal reconstruction using greedy algorithms in the compressive sensing (CS) framework. In particular, we obtain an improved bound over the best known results on the restricted isometry constant for successful recovery of sparse signals using orthogonal matching pursuit (OMP).