A Fast Algorithm for Low Rank + Sparse column-wise Compressive Sensing

Abstract

This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an n q matrix, ^* =[ _1^*, _2^*, , _q^*] from m independent linear projections of each of its q columns, given by _k :=_k_k^*, k [q]. Here, _k is an m-length vector with m < n. We assume that the matrix ^* can be decomposed as ^*=^*+^*, where ^* is a low rank matrix of rank r << (n,q) and ^* is a sparse matrix. Each column of contains non-zero entries. The matrices _k are known and mutually independent for different k. To address this recovery problem, we propose a novel fast GD-based solution called AltGDmin-LR+S, which is memory and communication efficient. We numerically evaluate its performance by conducting a detailed simulation-based study.

Tasks

Reproductions