Sparse Bayesian Learning for Robust PCA: Algorithms and Analyses | IEEE Journals & Magazine | IEEE Xplore

Sparse Bayesian Learning for Robust PCA: Algorithms and Analyses


Abstract:

In this paper, we propose a new Bayesian model to solve the Robust PCA problem - recovering the underlying low-rank matrix and sparse matrix from their noisy compositions...Show More

Abstract:

In this paper, we propose a new Bayesian model to solve the Robust PCA problem - recovering the underlying low-rank matrix and sparse matrix from their noisy compositions. We first derive and analyze a new objective function, which is proven to be equivalent to the fundamental objective of minimizing the “rank+sparsity”. To solve this objective, we develop a concise Sparse Bayesian Learning (SBL) method that makes minimal assumptions and effectively deals with the requirements of the problem. The concise modeling allows simple and effective Empirical Bayesian inference via maximum a posteriori expectation-maximization (MAP-EM). We further propose a modified SBL method that additionally utilizes the sparsity pattern information of the outliers in the Robust PCA problem. Simulation studies demonstrate the superiority of the proposed methods over the existing state-of-the-art methods. The efficacy of the proposed methods is further verified through two image processing tasks.
Published in: IEEE Transactions on Signal Processing ( Volume: 67, Issue: 22, 15 November 2019)
Page(s): 5837 - 5849
Date of Publication: 07 October 2019

ISSN Information:

Funding Agency:


References

References is not available for this document.