Correction of Corrupted Columns Through Fast Robust Hankel Matrix Completion

Shuai Zhang, Meng Wang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

This paper studies the robust matrix completion (RMC) problem with the objective to recover a low-rank matrix from partial observations that may contain significant errors. If all the observations in one column are erroneous, existing RMC methods can locate the corrupted column at best but cannot recover the actual data in that column. Low-rank Hankel matrices characterize the additional correlations among columns besides the low-rankness and exist in power system monitoring, magnetic resonance imaging (MRI) imaging, and array signal processing. Exploiting the low-rank Hankel property, this paper develops an alternating-projection-based fast algorithm to solve the nonconvex RMC problem. The algorithm converges to the ground-truth low-rank matrix with a linear rate even when all the measurements in a constant fraction of columns are corrupted. The required number of observations is significantly less than the existing bounds for the conventional RMC. Numerical results are reported to evaluate the proposed algorithm.

Original languageEnglish (US)
Article number8663310
Pages (from-to)2580-2594
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume67
Issue number10
DOIs
StatePublished - May 15 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Matrix completion
  • low-rank Hankel matrix
  • matrix decomposition
  • non-convex method

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