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

arXiv: https://arxiv.org/abs/2103.02356 · HTML: https://mlsanity.com/paper/2103.02356/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors](https://mlsanity.com/paper/2309.09032/) (2023)
- [Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares](https://mlsanity.com/paper/2306.04961/) (2023)

## Abstract (arXiv)

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.