Two step recovery of jointly sparse and low-rank matrices: theoretical guarantees

TL;DR

This paper proposes a two-step algorithm with theoretical guarantees for recovering matrices that are both jointly sparse and low-rank from undersampled column measurements, validated on CINE data.

Contribution

It introduces a novel two-step recovery method combining subspace estimation and least squares, with proven theoretical guarantees for joint sparsity and low-rank matrices.

Findings

Successful recovery of CINE data from undersampled measurements

Good recovery performance under specified sampling conditions

Theoretical guarantees support the algorithm's effectiveness

Abstract

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of the matrix is solved using a simple least square algorithm. The results are verified in the context of recovering CINE data from undersampled measurements; we obtain good recovery when the sampling conditions are satisfied.