# Deep Unfolded Tensor Robust PCA with Self-supervised Learning

arXiv: https://arxiv.org/abs/2212.11346 · HTML: https://mlsanity.com/paper/2212.11346/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 21 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent](https://mlsanity.com/paper/2005.08898/) (2020)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [On Tensor Completion via Nuclear Norm Minimization](https://mlsanity.com/paper/1405.1773/) (2014)
- [Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence](https://mlsanity.com/paper/1904.10020/) (2019)
- [Low-Rank Matrix Recovery with Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Number](https://mlsanity.com/paper/2010.13364/) (2020)
- [Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements](https://mlsanity.com/paper/2104.14526/) (2021)
- [Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent](https://mlsanity.com/paper/2206.09109/) (2022)
- [A Deep-Unfolded Reference-Based RPCA Network For Video Foreground-Background Separation](https://mlsanity.com/paper/2010.00929/) (2020)
- [Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations](https://mlsanity.com/paper/1510.04747/) (2015)
- [Tensor Robust Principal Component Analysis: Better recovery with atomic norm regularization](https://mlsanity.com/paper/1901.10991/) (2019)

## Built on by (most cited first, 7 of 7)

- [Generalized Parallel Scaling with Interdependent Generations](https://mlsanity.com/paper/2510.01143/) (2025)
- [A Lightweight Transformer for Faster and Robust EBSD Data Collection](https://mlsanity.com/paper/2308.09693/) (2023)
- [Leveraging Multimodal Diffusion Models to Accelerate Imaging with Side Information](https://mlsanity.com/paper/2410.05143/) (2024)
- [Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA](https://mlsanity.com/paper/2501.04565/) (2025)
- [Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling](https://mlsanity.com/paper/2409.11529/) (2024)
- [Robust Principal Component Completion](https://mlsanity.com/paper/2603.25132/) (2026)
- [Multimodal Diffusion to Mutually Enhance Polarized Light and Low Resolution EBSD Data](https://mlsanity.com/paper/2604.22212/) (2026)

## Abstract (arXiv)

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While powerful, existing tensor RPCA algorithms can be difficult to use in practice, as their performance can be sensitive to the choice of additional hyperparameters, which are not straightforward to tune. In this paper, we describe a fast and simple self-supervised model for tensor RPCA using deep unfolding by only learning four hyperparameters. Despite its simplicity, our model expunges the need for ground truth labels while maintaining competitive or even greater performance compared to supervised deep unfolding. Furthermore, our model is capable of operating in extreme data-starved scenarios. We demonstrate these claims on a mix of synthetic data and real-world tasks, comparing performance against previously studied supervised deep unfolding methods and Bayesian optimization baselines.