Improved Coherence Index-Based Bound in Compressive Sensing

TL;DR

This paper improves the coherence index-based bound for signal uniqueness in compressive sensing, enhancing the reliability of sparse signal reconstruction with less conservative criteria.

Contribution

It introduces a less conservative coherence index-based lower bound for sparsity in matching pursuit algorithms and extends the results to signals in two orthonormal bases.

Findings

Derived a new, less conservative coherence index-based lower bound.

Generalized the results to signals in two orthonormal bases.

Enhanced the practical reliability of sparse signal reconstruction.

Abstract

Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible calculation, coherence index is one of very few CS metrics with a considerable practical importance. In this paper, we propose an improvement of the coherence based uniqueness relation for the matching pursuit algorithms. Starting from a simple and intuitive derivation of the standard uniqueness condition based on the coherence index, we derive a less conservative coherence index-based lower bound for signal sparsity. The results are generalized to the uniqueness condition of the $l_0$-norm minimization for a signal represented in two orthonormal bases.