Iterative hard thresholding for low-rank recovery from rank-one projections

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.