Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

TL;DR

This paper introduces efficient methods for recovering sparse parameters in low-rank linear models by combining support estimation with matrix completion, significantly reducing computational costs while maintaining high accuracy.

Contribution

The paper proposes a novel unified four-step approach that integrates support estimation with matrix completion for sparse parameter recovery in low-rank models.

Findings

Augmented method outperforms two-step approach in accuracy.

Proposed methods require less computation than natural techniques.

Simulation results validate the effectiveness of the unified approach.

Abstract

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion on the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.