When is P such that l_0-minimization Equals to l_p-minimization

TL;DR

This paper characterizes the conditions under which the solutions to l_0-minimization and l_p-minimization coincide, providing analysis, proofs, and examples to validate these conditions.

Contribution

It introduces an explicit analysis expression for p(A,b) ensuring solution equivalence between l_0 and l_p minimizations, along with a rigorous proof.

Findings

Derived an analysis expression for p(A,b)

Proved the conditions for solution equivalence

Validated results with two example cases

Abstract

In this paper, we present an analysis expression of p(A,b) such that the unique solution to l_0-minimization also can be the unique solution to l_p-minimization for any 0<p<p(A,b). Furthermore, the main contribution of this paper isn't only the analysis expressed of such p^(A,b) but also its proof. Finally, we display the results of two examples to confirm the validity of our conclusions