Abstract: Low-rank matrix models play a prominent role in many areas of applied mathematics, statistics and data science. For example, they can be used for matrix recovery from incomplete information. We consider the particular task of recovering a row-sparse low-rank matrix from linear measurements, which arises for instance in sparse blind deconvolution. The ideal goal is to ensure recovery using only a minimal number of measurements with respect to the joint low-rank and sparsity constraint. We present modifications of the iterative hard thresholding (IHT) method for this task. In particular, a manifold version of IHT is proposed which significantly reduces the computational cost of the gradient projection in the case of rank-one measurements. We also consider a manifold proximal gradient method for the special case of unknown sparsity.
Gradient methods for row-sparse and low-rank matrix recovery
24.05.2022 16:20 - 17:05
Organiser:
R. I. Boţ
Location: