A variational approach to stable principal component pursuit

Abstract

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.

arXiv comment10 pages, 5 figures

References in corpus (1)

• The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

Cited by in corpus (15)

• Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery
• Parametric Bilinear Generalized Approximate Message Passing
• Basis Pursuit Denoise with Nonsmooth Constraints
• Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis
• Adaptive Quantile Low-Rank Matrix Factorization
• Denoising-based Turbo Message Passing for Compressed Video Background Subtraction
• An ADMM Approach to Masked Signal Decomposition Using Subspace Representation
• Tensor Robust Principal Component Analysis: Better recovery with atomic norm regularization
• Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
• Blind Community Detection from Low-rank Excitations of a Graph Filter
• Decentralized Dictionary Learning Over Time-Varying Digraphs
• Subspace Learning in The Presence of Sparse Structured Outliers and Noise
• Compressive PCA for Low-Rank Matrices on Graphs
• Image Segmentation Using Subspace Representation and Sparse Decomposition
• Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants