Identification of Matrices having a Sparse Representation

TL;DR

This paper investigates methods for recovering matrices from their action on vectors using sparse representations, focusing on time-frequency shift dictionaries and random matrices, with applications in communications channel estimation.

Contribution

It introduces recovery results for Basis Pursuit applied to time-frequency shift dictionaries and various random matrix dictionaries, advancing matrix identification techniques.

Findings

Successful recovery with Basis Pursuit for time-frequency shift matrices

Effective reconstruction results for random matrix dictionaries

Enhanced methods for channel estimation in communications

Abstract

We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of efficient reconstruction techniques such as Basis Pursuit. Of particular interest is the dictionary of time-frequency shift matrices and its role for channel estimation and identification in communications engineering. We present recovery results for Basis Pursuit with the time-frequency shift dictionary and various dictionaries of random matrices.