Riemannian thresholding methods for row-sparse and low-rank matrix recovery
Optimization and Control
2022-10-03 v2 Numerical Analysis
Numerical Analysis
Abstract
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces computational cost of the gradient projection in the case of rank-one measurement operators, which have concrete applications in blind deconvolution. Experimental results are reported that show near-optimal recovery for Gaussian and rank-one measurements, and that adaptive stepsizes give crucial improvement. A Riemannian proximal gradient method is derived for the special case of unknown sparsity.
Cite
@article{arxiv.2103.02356,
title = {Riemannian thresholding methods for row-sparse and low-rank matrix recovery},
author = {Henrik Eisenmann and Felix Krahmer and Max Pfeffer and André Uschmajew},
journal= {arXiv preprint arXiv:2103.02356},
year = {2022}
}