학술논문
Improved Coherence Index-Based Bound in Compressive Sensing
Document Type
Periodical
Author
Source
IEEE Signal Processing Letters IEEE Signal Process. Lett. Signal Processing Letters, IEEE. 28:1110-1114 2021
Subject
Language
ISSN
1070-9908
1558-2361
1558-2361
Abstract
Within the compressive sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements, whereby reliability of the solution is determined by its uniqueness. With its mathematically tractable and feasible calculation, the coherence index is one of very few CS uniqueness metrics with considerable practical importance. 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.