Robust Low-Rank Matrix Recovery Fusing Local-Smoothness

Liu, Xinling; Hou, Jingyao; Wang, Jianjun

doi:10.1109/lsp.2022.3229555

Cited by 7 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the frames of the background are highly correlated in general, it can be modeled as a low-rank tensor. While the foreground part can be modeled as a sparse tensor since the moving objects often occupy a small part of each video frame (Lu et al 2020;Liu et al 2023). Analogously, a face image with disguise (e.g., sunglasses) can be regarded as a superposition of a noiseless face image (lying in a low-dimensional subspace (Wright et al 2009)) and the occlusion part (deemed as a sparse matrix).…”

Section: Introductionmentioning

confidence: 99%

Superposed Atomic Representation for Robust High-Dimensional Data Recovery of Multiple Low-Dimensional Structures

Wang

2024

AAAI

View full text Add to dashboard Cite

This paper proposes a unified Superposed Atomic Representation (SAR) framework for high-dimensional data recovery with multiple low-dimensional structures. The data can be in various forms ranging from vectors to tensors. The goal of SAR is to recover different components from their sum, where each component has a low-dimensional structure, such as sparsity, low-rankness or be lying a low-dimensional subspace. Examples of SAR include, but not limited to, Robust Sparse Representation (RSR), Robust Principal Component Analysis (RPCA), Tensor RPCA (TRPCA), and Outlier Pursuit (OP). We establish the theoretical guarantee for SAR. To further improve SAR, we also develop a Weighted SAR (WSAR) framework by paying more attention and penalizing less on significant atoms of each component. An effective optimization algorithm is devised for WSAR and the convergence of the algorithm is rigorously proved. By leveraging WSAR as a general platform, several new methods are proposed for high-dimensional data recovery. The experiments on real data demonstrate the superiority of WSAR for various data recovery problems.

show abstract

Section: Introductionmentioning

confidence: 99%