An Improved Lower Bound of The Spark With Application

TL;DR

This paper introduces a new lower bound for the spark of a matrix, which enhances the criteria for the uniqueness of sparse solutions in underdetermined linear systems.

Contribution

It presents a novel lower bound for the spark and applies it to establish a new criterion for sparse solution uniqueness.

Findings

New lower bound of spark derived

Improved criterion for sparse solution uniqueness

Enhanced understanding of linear system solutions

Abstract

Spark plays a great role in studying uniqueness of sparse solutions of the underdetermined linear equations. In this article, we derive a new lower bound of spark. As an application, we obtain a new criterion for the uniqueness of sparse solutions of linear equations.