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A Survey on Matrix Completion: Perspective of Signal Processing

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arxiv 1901.10885 v3 pith:GAADPDL2 submitted 2019-01-25 eess.SP

Xiao Peng Li , Lei Huang , Hing Cheung So , Bo Zhao This is my paper · ORCID
classification eess.SP
keywords matrixprocessingsignalalgorithmsapplicationcompletionoptimizationperspective
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fast exact recovery of noisy matrix from few entries: the infinity norm approach

    math.ST 2025-01 conditional novelty 8.0 of 10

    A truncated-SVD-plus-rounding algorithm achieves exact recovery of noisy low-rank matrices under only low rank, incoherence, and sufficient sampling, with a new infinity-norm perturbation theorem.

  2. Sample-efficient inductive matrix completion with noise and inexact side-information

    stat.ML 2026-05 unverdicted novelty 7.0 of 10

    Nonconvex projected gradient descent for noisy inductive matrix completion achieves linear convergence and order-optimal error at sample complexity scaling with side-information dimension a instead of ambient dimension n.

  3. Deep Image Prior Assisted ISAR Imaging for Missing Data Case

    eess.IV 2025-07 conditional novelty 5.0 of 10

    A no-training deep image prior, applied separately to real and imaginary parts of ISAR radar data, reconstructs missing entries and outperforms IALM, 2D-SL0, and NNM at high missing ratios.

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