# Robust Principal Component Completion

arXiv: https://arxiv.org/abs/2603.25132 · HTML: https://mlsanity.com/paper/2603.25132/

## 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.

## Builds on (most cited first, 18 of 18)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction](https://mlsanity.com/paper/2105.10446/) (2021)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Fast Algorithms for Robust PCA via Gradient Descent](https://mlsanity.com/paper/1605.07784/) (2016)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)
- [Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements](https://mlsanity.com/paper/1503.01868/) (2015)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Tensor Train Factorization and Completion under Noisy Data with Prior Analysis and Rank Estimation](https://mlsanity.com/paper/2010.06564/) (2020)
- [Deep Unfolded Tensor Robust PCA with Self-supervised Learning](https://mlsanity.com/paper/2212.11346/) (2022)
- [A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring](https://mlsanity.com/paper/2409.18731/) (2024)
- [Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way](https://mlsanity.com/paper/2101.02931/) (2021)
- [Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtraction](https://mlsanity.com/paper/2309.15576/) (2023)

## 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.