# Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee

arXiv: https://arxiv.org/abs/2203.16328 · HTML: https://mlsanity.com/paper/2203.16328/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [Background Subtraction in Real Applications: Challenges, Current Models and Future Directions](https://mlsanity.com/paper/1901.03577/) (2019)
- [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)
- [Towards Benchmarking Scene Background Initialization](https://mlsanity.com/paper/1506.04051/) (2015)
- [Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset](https://mlsanity.com/paper/1511.01245/) (2015)
- [Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterion](https://mlsanity.com/paper/2010.11740/) (2020)
- [Riemannian Stochastic Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel Manifold](https://mlsanity.com/paper/2005.01209/) (2020)
- [Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method](https://mlsanity.com/paper/2008.07740/) (2020)

## Built on by (most cited first, 5 of 5)

- [Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modeling](https://mlsanity.com/paper/2404.04403/) (2024)
- [Global-local Fourier Neural Operator for Accelerating Coronal Magnetic Field Model](https://mlsanity.com/paper/2405.12754/) (2024)
- [Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data](https://mlsanity.com/paper/2309.03439/) (2023)
- [On Model Compression for Neural Networks: Framework, Algorithm, and Convergence Guarantee](https://mlsanity.com/paper/2303.06815/) (2023)
- [Robust Foreground-Background Separation for Severely-Degraded Videos Using Convolutional Sparse Representation Modeling](https://mlsanity.com/paper/2506.17838/) (2025)

## Abstract (arXiv)

The objective of this study is to address the problem of background/foreground separation with missing pixels by combining the video acquisition, video recovery, background/foreground separation into a single framework. To achieve this, a smooth robust tensor completion (SRTC) model is proposed to recover the data and decompose it into the static background and smooth foreground, respectively. Specifically, the static background is modeled by the low-rank tucker decomposition and the smooth foreground (moving objects) is modeled by the spatiotemporal continuity, which is enforced by the total variation regularization. An efficient algorithm based on tensor proximal alternating minimization (tenPAM) is implemented to solve the proposed model with global convergence guarantee under very mild conditions. Extensive experiments on real data demonstrate that the proposed method significantly outperforms the state-of-the-art approaches for background/foreground separation with missing pixels.