  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.
