Iterative Hard Thresholding for Low-Rank Recovery from Rank-One Projections

TL;DR

This paper introduces a new iterative hard thresholding algorithm tailored for low-rank matrix recovery from rank-one projections, especially effective when traditional RIP conditions do not hold, with proven stability and demonstrated numerical performance.

Contribution

The paper presents a novel variation of iterative hard thresholding that succeeds under measurement conditions where standard RIP-based methods fail, expanding the applicability of low-rank recovery techniques.

Findings

Algorithm is stable and robust under challenging measurement conditions.

Numerical experiments confirm the effectiveness of the proposed method.

Applicable to subexponential and subgaussian rank-one measurements.

Abstract

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to succeed in situations where the standard rank-restricted isometry property fails, e.g. in case of subexponential unstructured measurements or of subgaussian rank-one measurements. The stability and robustness of the algorithm are established based on distinctive matrix-analytic ingredients and its performance is substantiated numerically.