A Survey on Matrix Completion: Perspective of Signal Processing

TL;DR

This survey comprehensively reviews matrix completion techniques from a signal processing perspective, categorizing optimization problems, algorithms, and applications to provide a clear understanding of recent advances.

Contribution

It offers a structured overview of matrix completion approaches, including problem grouping, algorithm types, and application fields, from the signal processing viewpoint.

Findings

Six optimization problem groups for matrix completion are identified.

Four key optimization algorithms for MC are reviewed.

Three application fields of MC are analyzed and evaluated.

Abstract

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and thereby receives much attention in the past several years. There are plenty of works addressing the behaviors and applications of MC methodologies. This work provides a comprehensive review for MC approaches from the perspective of signal processing. In particular, the MC problem is first grouped into six optimization problems to help readers understand MC algorithms. Next, four representative types of optimization algorithms solving the MC problem are reviewed. Ultimately, three different application fields of MC are described and evaluated.