Iterative Hard Thresholding for Low-Rank Recovery from Rank-One Projections
This work addresses the problem of low-rank matrix recovery from challenging measurement models, offering a practical algorithm for compressive sensing applications where existing methods struggle.
The paper proposes a novel iterative hard thresholding algorithm for low-rank matrix recovery from compressive linear measurements, designed to succeed where standard rank-restricted isometry property fails, such as with subexponential unstructured or subgaussian rank-one measurements. The algorithm's stability and robustness are established theoretically and demonstrated numerically.
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.