Alternating Strategies Are Good For Low-Rank Matrix Reconstruction

TL;DR

This paper introduces a novel combined alternating optimization approach that improves low-rank matrix reconstruction, especially for structured matrices like Hankel, outperforming traditional methods based on numerical simulations.

Contribution

It proposes merging ALS with ADMM strategies to enhance low-rank matrix recovery, particularly for structured matrices.

Findings

Outperforms existing ALS strategies in simulations

Effective for structured matrices like Hankel

Demonstrates improved reconstruction accuracy

Abstract

This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating direction method of multipliers (ADMM) to recover structured low-rank matrices, such as Hankel structure. We show that merging these two alternating strategies leads to a better performance than the existing alternating least squares (ALS) strategy. The performance is evaluated via numerical simulations.