Reducing Basis Mismatch in Harmonic Signal Recovery via Alternating Convex Search

TL;DR

This paper introduces an iterative biconvex search algorithm that mitigates basis mismatch in harmonic signal recovery, improving estimation accuracy over existing methods by combining $\, ext{l}_1$-minimization with maximum likelihood estimation.

Contribution

It proposes a novel iterative algorithm that addresses basis mismatch in harmonic signal recovery, enhancing accuracy beyond current state-of-the-art techniques.

Findings

Outperforms existing methods in harmonic signal recovery.

Effectively reduces basis mismatch errors.

Demonstrates robustness across varying sparsity levels.

Abstract

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact signal model can result in dramatic increases in estimation error; this is the so-called "basis mismatch" problem. This work provides one possible solution to this problem in the form of an iterative, biconvex search algorithm. The approach uses standard $\ell_1$-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art.