Sparse free deconvolution under unknown noise level via eigenmatrix

TL;DR

This paper introduces a method for spectral estimation of sparse measures under unknown noise levels using eigenmatrix techniques, with a novel approach to estimate noise level via singular value optimization, demonstrated through numerical experiments.

Contribution

It presents a new approach combining eigenmatrix methods with an optimization for unknown noise levels in free deconvolution problems.

Findings

Effective noise level estimation via singular value optimization.

Successful application to additive and multiplicative free deconvolution.

Numerical results validate the proposed method.

Abstract

This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is determined, the free deconvolution reduces the problem to an unstructured sparse recovery problem to which the eigenmatrix method can be applied. To determine the unknown noise level, we propose an optimization problem based on the singular values of an intermediate matrix of the eigenmatrix method. Numerical results are provided for both the additive and multiplicative free deconvolutions.