Volume 53, pp. 481-499, 2020.

Matrix completion for matrices with low-rank displacement

Damiana Lazzaro and Serena Morigi


The matrix completion problem consists in the recovery of a low-rank or approximately low-rank matrix from a sampling of its entries. The solution rank is typically unknown, and this makes the problem even more challenging. However, for a broad class of interesting matrices with so-called displacement structure, the originally ill-posed completion problem can find an acceptable solution by exploiting the knowledge of the associated displacement rank. The goal of this paper is to propose a variational non-convex formulation for the low-rank matrix completion problem with low-rank displacement and to apply it to important classes of medium-large scale structured matrices. Experimental results show the effectiveness and efficiency of the proposed approach for Toeplitz and Hankel matrix completion problems.

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Key words

matrix completion, low-rank matrices, displacement rank, non-convex optimization

AMS subject classifications

65K10, 65F22, 15A29

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