PETRELS-ADMM: Robust Subspace Tracking with Missing Data and Outliers

We propose a novel algorithm called PETRELS-ADMM to deal with subspace tracking in the presence of outliers and missing data. The proposed approach consists of two main stages: outlier rejection and subspace estimation. Particularly, we first use ADMM solver for detecting outliers living in the measurement data in an efficient online way and then improve the well-known PETRELS algorithm to update the underlying subspace in the missing data context.

Updates:

Jan 2021: Create this repository.
Oct 2021: Reorganize the entire repository.
Jun 2022: Add a demo DEMO_SEP_Main_Synthetic.m (avoids the warning message from MATLAB R202x caused by ReProCS and NORST)

DEMO

Run “DEMO_SEP_Main.m” (MATLAB R201x) or “DEMO_SEP_Main_Synthetic.m” (MATLAB R202x) for synthetic data.
Run “DEMO_Video.m” for real data: Video data can be downloaded from Releases or here.

State-of-the-art algorithms for comparison

GRASTA: https://sites.google.com/site/hejunzz/grasta
ROSETA: http://www.merl.com/research/license#ROSETA
ReProCS: https://github.com/praneethmurthy/ReProCS
NORST: https://github.com/praneethmurthy/NORST

Some results

Synthetic data

untitled

Video background-foreground separation application

References

This code is free and open source for research purposes. If you use this code, please acknowledge the following papers.

[1] L.T. Thanh, V.D. Nguyen, N. L. Trung and K. Abed-Meraim. “Robust Subspace Tracking with Missing Data and Outliers: Novel Algorithm with Convergence Guarantee”. IEEE Trans. Signal Process., 2021. [DOI],[PDF].

[2] L.T. Thanh, V.D Nguyen, N.L. Trung and K. Abed-Meraim. “Robust Subspace Tracking with Missing Data and Outliers via ADMM”. Proc. 27th EUSIPCO, 2019. [DOI],[PDF].