Fast Robust Matrix Completion via Entry-Wise ℓ0-Norm Minimization

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6 Scopus Citations
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Original languageEnglish
Pages (from-to)7199-7212
Number of pages14
Journal / PublicationIEEE Transactions on Cybernetics
Issue number11
Online published6 Dec 2022
Publication statusPublished - Nov 2023



Matrix completion (MC) aims at recovering missing entries, given an incomplete matrix. Existing algorithms for MC are mainly designed for noiseless or Gaussian noise scenarios and, thus, they are not robust to impulsive noise. For outlier resistance, entry-wise p-norm with 0 < < 2 and M-estimation are two popular approaches. Yet the optimum selection of p for the entrywise p-norm-based methods is still an open problem. Besides, M-estimation is limited by a breakdown point, that is, the largest proportion of outliers. In this article, we adopt entrywise 0-norm, namely, the number of nonzero entries in a matrix, to separate anomalies from the observed matrix. Prior to separation, the Laplacian kernel is exploited for outlier detection, which provides a strategy to automatically update the entrywise ℓ0-norm penalty parameter. The resultant multivariable optimization problem is addressed by block coordinate descent (BCD), yielding 0-BCD and 0-BCD-F. The former detects and separates outliers, as well as its convergence is guaranteed. In contrast, the latter attempts to treat outlier-contaminated elements as missing entries, which leads to higher computational efficiency. Making use of majorization–minimization (MM), we further propose 0-BCD-MM and 0-BCD-MM-F for robust non-negative MC where the nonnegativity constraint is handled by a closed-form update. Experimental results of image inpainting and hyperspectral image recovery demonstrate that the suggested algorithms outperform several state-of-the-art methods in terms of recovery accuracy and computational efficiency.

Research Area(s)

  • ℓ0-norm optimization, matrix completion (MC), non-negative MC (NMC), outlier detection, robust recovery

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