Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices

• DOI: 10.1109/tpami.2022.3204203
• Publication Date: 2022-09-05T20:15:00Z
• Authors: Jiangjun Peng; Yao Wang; Hongying Zhang; Jianjun Wang; Deyu Meng
• Keywords: Smoothness; Regularization; Matrix (chemical analysis)

It is known that the decomposition in low-rank and sparse matrices ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L+S</b> for short) can be achieved by several Robust PCA techniques. Besides low rankness, local smoothness xmlns:xlink="http://www.w3.org/1999/xlink">LSS</b> ) a vitally essential prior many real-world matrix data such as hyperspectral images surveillance videos, which makes have low-rankness property at same time. This poses an interesting question: Can we make terms of xmlns:xlink="http://www.w3.org/1999/xlink">L&amp;LSS +S</b> form exactly? To address this issue, propose paper new RPCA model based on three-dimensional correlated total variation regularization (3DCTV-RPCA fully exploiting encoding expression underlying joint matrices. Specifically, using modification Golfing scheme, prove under some mild assumptions, proposed 3DCTV-RPCA decompose both components exactly, should first theoretical guarantee among all related methods combining rankness smoothness. In addition, utilizing Fast Fourier Transform (FFT), efficient ADMM algorithm with solid convergence solving resulting optimization problem. Finally, series experiments simulations real applications are carried out to demonstrate general validity model.