Matrix Recipes for Hard Thresholding Methods

TL;DR

This paper introduces new low-rank recovery algorithms using hard thresholding for linear inverse problems, emphasizing efficiency, convergence guarantees, and improved performance over existing methods.

Contribution

It proposes a versatile framework for low-rank recovery algorithms with acceleration techniques and theoretical convergence analysis.

Findings

Algorithms achieve better accuracy and lower complexity.

Acceleration schemes improve computational efficiency.

Theoretical guarantees ensure convergence under mild conditions.

Abstract

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for different configurations to achieve complexity vs. accuracy tradeoffs. Moreover, we study acceleration schemes via memory-based techniques and randomized, $\epsilon$-approximate matrix projections to decrease the computational costs in the recovery process. For most of the configurations, we present theoretical analysis that guarantees convergence under mild problem conditions. Simulation results demonstrate notable performance improvements as compared to state-of-the-art algorithms both in terms of reconstruction accuracy and computational complexity.