Riemannian thresholding methods for row-sparse and low-rank matrix recovery

Henrik Eisenmann, Felix Krahmer, Max Pfeffer, and André Uschmajew

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Submission date: 03. Mar. 2021 (revised version: September 2022)
Pages: 26
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Link to arXiv: See the arXiv entry of this preprint.

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.