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Robust Principal Component Completion

arXiv 2603.25132 ↗First posted 26 Mar 2026cs.CV cs.LGcited by 0

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Abstract (arXiv)

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank background. To address this mismatch, a new framework is proposed in which the sparse component is identified indirectly through determining its support. This approach, called robust principal component completion (RPCC), is solved via variational Bayesian inference applied to a fully probabilistic Bayesian sparse tensor factorization. Convergence to a hard classifier for the support is shown, thereby eliminating the post-hoc thresholding required of most prior RPCA-driven approaches. Experimental results reveal that the proposed approach delivers near-optimal estimates on synthetic data as well as robust foreground-extraction and anomaly-detection performance on real color video and hyperspectral datasets, respectively. Source implementation and Appendices are available at https://github.com/WongYinJ/BCP-RPCC.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 18 of its 52 references that are in the map. First posted on arXiv 26 Mar 2026.

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18 of 52 references.

References · 18

  1. 2016Tensor Ring Decompositioncited by 127
  2. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 112
  3. 2021ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reductioncited by 84
  4. 2014Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determinationcited by 65
  5. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 46
  6. 2014Non-convex Robust PCAcited by 41
  7. 2023Guaranteed Tensor Recovery Fused Low-rankness and Smoothnesscited by 41
  8. 2016Fast Algorithms for Robust PCA via Gradient Descentcited by 39
  9. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  10. 2014Bayesian Robust Tensor Factorization for Incomplete Multiway Datacited by 22
  11. 2018Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applicationscited by 16
  12. 2015Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurementscited by 14
6 more
  1. 2025RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentationcited by 12
  2. 2020Tensor Train Factorization and Completion under Noisy Data with Prior Analysis and Rank Estimationcited by 7
  3. 2022Deep Unfolded Tensor Robust PCA with Self-supervised Learningcited by 7
  4. 2024A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurringcited by 5
  5. 2021Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Waycited by 4
  6. 2023Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtractioncited by 4

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