CORPCA

Compressive Online Robust Principal Component Analysis with Multiple Prior Information (CORPCA)

Version 1.1,  Jan. 24, 2017
Implementations by Huynh Van Luong, Email: huynh.luong@fau.de,
Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg.

Please see LICENSE for the full text of the license.

Please cite these publications:

Huynh Van Luong, N. Deligiannis, J. Seiler, S. Forchhammer, and A. Kaup, "Compressive Online Robust Principal Component Analysis with Multiple Prior Information," in IEEE Global Conference on Signal and Information Processing (GlobalSIP 2017), Montreal, Canada, Nov. 2017.

Huynh Van Luong, Nikos Deligiannis, Jürgen Seiler, Søren Forchhammer, and André Kaup, "Compressive Online Robust Principal Component Analysis Via n-l1 Minimization," IEEE Transactions on Image Processing, vol. 27, no. 9, pp. 4314-4329, Sep. 2018.

Solving the problem

$\small \min_{\boldsymbol{x}_{t},\boldsymbol{v}_{t}}\Big\{H(\boldsymbol{x}_{t},\boldsymbol{v}_{t})=\frac{1}{2}\|\mathbf{\Phi}(\boldsymbol{x}_{t}+\boldsymbol{v}_{t})-\boldsymbol{y}_{t}\|^{2}_{2} +\lambda\mu\sum\limits_{j=0}^{J}\beta_{j}\|\mathbf{W}_{j}(\boldsymbol{x}_{t}-\boldsymbol{z}_{j})\|_{1}+ \mu\Big\|[\boldsymbol{B}_{t-1}\boldsymbol{v}_{t}]\Big\|_{*}\Big\}$

Inputs:

$\boldsymbol{y}_{t}\in \mathbb{R}^{m}$ : A vector of observations/data
$\mathbf{\Phi}\in \mathbb{R}^{m\times n}$ : A measurement matrix
$\boldsymbol{y}_{t}\in \mathbb{R}^{n}$ : The foreground prior
$\boldsymbol{B}_{t-1}\in \mathbb{R}^{n\times d}$ : A matrix of the background prior, which could be initialized by previous backgrounds

Outputs:

$\boldsymbol{x}_{t},\boldsymbol{v}_{t}\in\mathbb{R}^{n}$ : Estimates of foreground and background
$\boldsymbol{Z}_{t}:=\{\boldsymbol{z}_{j}=\boldsymbol{x}_{t-J+j}\}$ : The updated foreground prior
$\boldsymbol{B}_{t}\in \mathbb{R}^{n\times d}$ : The updated background prior

Source code files: (for C++ codes, please refer to corpca-of)

corpca.m: The function for CORPCA
usageDemo_corpca.m: One demo to run CORPCA
dataGeneration.m: Generating data for numerical simulations
inexact_alm_rpca: This folder contains an offline RPCA (batch-based) code for initializing background and foreground prior information

Experimental results:

videos: This folder consists of original test videos and separated sequences
- Please see file videos/videoList.md for more details
fullRateComparisons_BootstrapCurtain.pptx: a presentation of video separation comparisons (Bootstrap and Curtain) for CORPCA vs. RPCA, GRASTA, and ReProCS with full data access
compressiveRatesCORPCAvsReProCS_Bootstrap.pptx: a presentation of video separation comparisons (Bootstrap) for CORPCA vs. ReProCS with different measurement rates m/n
compressiveRatesCORPCAvsReProCS_Curtain.pptx: a presentation of video separation comparisons (Curtain) for CORPCA vs. ReProCS with different measurement rates m/n

caesarcai/corpca

CORPCA