Exact Reconstruction Conditions for Regularized Modified Basis Pursuit

TL;DR

This paper derives exact recovery conditions for regularized modified basis pursuit, a sparse signal recovery method that handles support and value estimation errors, and compares its performance with related algorithms.

Contribution

It provides new exact recovery conditions for reg-mod-BP and analyzes when these are weaker than conditions for modified-CS and BP.

Findings

Derived exact recovery conditions for reg-mod-BP.

Compared conditions with modified-CS and BP through simulations.

Identified scenarios where reg-mod-BP outperforms or matches existing methods.

Abstract

In this correspondence, we obtain exact recovery conditions for regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified-CS or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the sparse recovery problem when both an erroneous estimate of the signal's support, denoted by $T$, and an erroneous estimate of the signal values on $T$ are available.