Recovery of Sparse and Low Rank Components of Matrices Using Iterative Method with Adaptive Thresholding

TL;DR

This paper introduces a fast iterative algorithm with adaptive thresholding for recovering sparse and low-rank matrix components, demonstrating competitive performance and low runtime in practical applications.

Contribution

It presents a novel iterative method with adaptive thresholding for matrix decomposition, improving speed and applicability over existing $ ext{l}_1$ norm approximation techniques.

Findings

The proposed method is faster than traditional $ ext{l}_1$ norm based approaches.

It performs well even with non-sparse noise in real applications.

Simulation results confirm low runtime and effective recovery.

Abstract

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it with one of the most common fast methods in which the rank and sparsity are approximated by $\ell_1$ norm. We also apply it to some real applications where the noise is not so sparse. The simulation results show that it has a suitable performance with low run-time.