Matrix Recipes for Hard Thresholding Methods

Authors:
Anastasios Kyrillidis;Volkan Cevher
Affiliations:
Laboratory for Information and Inference Systems, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland;Laboratory for Information and Inference Systems, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
Venue:
Journal of Mathematical Imaging and Vision
Year:
2014

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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, ∈-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.