# A variational approach to stable principal component pursuit

arXiv: https://arxiv.org/abs/1406.1089 · HTML: https://mlsanity.com/paper/1406.1089/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2014.

## Built on by (most cited first, 8 of 8)

- [LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning](https://mlsanity.com/paper/2311.12023/) (2023)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Seeing Through Clouds in Satellite Images](https://mlsanity.com/paper/2106.08408/) (2021)
- [GaLore+: Boosting Low-Rank Adaptation for LLMs with Cross-Head Projection](https://mlsanity.com/paper/2412.19820/) (2024)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Robust Dual-Graph Regularized Moving Object Detection](https://mlsanity.com/paper/2204.11939/) (2022)
- [Human Motion Detection Based on Dual-Graph and Weighted Nuclear Norm Regularizations](https://mlsanity.com/paper/2304.04879/) (2023)
- [Transformed ℓ1 Regularizations for Robust Principal Component Analysis: Toward a Fine-Grained Understanding](https://mlsanity.com/paper/2510.03624/) (2025)

## Abstract (arXiv)

We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthetic and real data experiments, that our approach offers advantages over the classical SPCP formulations in scalability and practical parameter selection.