lighting-zhu / tmp

Turbo-Type Message Passing Algorithms for Compressed Robust Principal Component Analysis

This repository contains the implementation of the Turbo-Type Message Passing Algorithms for Compressed Robust Principal Component Analysis algorithm proposed in the paper:

Z. Xue, X. Yuan and Y. Yang, "Turbo-Type Message Passing Algorithms for Compressed Robust Principal Component Analysis," in IEEE Journal of Selected Topics in Signal Processing, vol. 12, no. 6, pp. 1182-1196, Dec. 2018, doi: 10.1109/JSTSP.2018.2876621.https://doi.org/10.1109/ACCESS.2017.2697978)

Introduction

Turbo-type message passing (TMP) is a Bayesian message passing algorithm for the compressed RPCA problem. We show that the proposed TMP algorithm significantly outperforms the state-of-the-art compressed RPCA algorithms, and requires a much lower computational complexity.

Code Structure

TMP.m: Turbo-Type Message Passing Algorithm with the low-rank denoiser set as the best rank-r denoiser

• Input parameters
  • y: measurement vector
  • A: sensing matrix, here we implement it as a linear opeartor
  • At: transpose of sensing matrix A
  • params: parameters used in recovery

TMP_svt.m: Turbo-Type Message Passing Algorithm with the low-rank denoiser set as the singular value soft thresholding (SVST) denoiser

TMP_svht.m: Turbo-Type Message Passing Algorithm with the low-rank denoiser set as the singular value hard thresholding (SVHT) denoiser

soft_thresholding.m: soft thresholding denoiser

kernel_lin_1.m: SURE-LET denoiser used in this paper

div_svht.m: divergence calculation of SVHT denoiser

div_svt.m: divergence calculation of SVST denoiser

TMP_test.m: comparisons of TMP algorithms with different low-rank matrix denoisers

TMP_test2.m: comparisons of different algorithms for compressed robust principal component recovery including SPCP and SpaRCS (users should install SPCP and SpaRCS matlab packages first)

Citation

@ARTICLE{8502093,
  author={Z. {Xue} and X. {Yuan} and Y. {Yang}},
  journal={IEEE Journal of Selected Topics in Signal Processing}, 
  title={Turbo-Type Message Passing Algorithms for Compressed Robust Principal Component Analysis}, 
  year={2018},
  volume={12},
  number={6},
  pages={1182-1196},
  doi={10.1109/JSTSP.2018.2876621}}

Test Result

Run TMP_test2.m and set the comparison parameters to the settings in fig6 (left) and fig6 (right) of the paper, you will get the following result: