# Deep Unrolling for Nonconvex Robust Principal Component Analysis

arXiv: https://arxiv.org/abs/2307.05893 · HTML: https://mlsanity.com/paper/2307.05893/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Deep learning in ultrasound imaging](https://mlsanity.com/paper/1907.02994/) (2019)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Accelerated Alternating Projections for Robust Principal Component Analysis](https://mlsanity.com/paper/1711.05519/) (2017)
- [Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation](https://mlsanity.com/paper/2010.07422/) (2020)
- [A Deep-Unfolded Reference-Based RPCA Network For Video Foreground-Background Separation](https://mlsanity.com/paper/2010.00929/) (2020)
- [Robust PCA Unrolling Network for Super-resolution Vessel Extraction in X-ray Coronary Angiography](https://mlsanity.com/paper/2204.08466/) (2022)
- [Multimodal Unrolled Robust PCA for Background Foreground Separation](https://mlsanity.com/paper/2108.06031/) (2021)

## Built on by (most cited first, 2 of 2)

- [Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers](https://mlsanity.com/paper/2504.19000/) (2025)
- [Neural Ising Machines via Unrolling and Zeroth-Order Training](https://mlsanity.com/paper/2602.00302/) (2026)

## Abstract (arXiv)

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating projection algorithm which aims to solve RPCA in its nonconvex form. The proposed procedure combines benefits of deep neural networks and the interpretability of the original algorithm and it automatically learns hyperparameters. We demonstrate the unrolled algorithm's effectiveness on synthetic datasets and also on a face modeling problem, where it leads to both better numerical and visual performances.