Robust Bayesian compressed sensing with outliers

Qian Wan, Huiping Duan, Jun Fang, Hongbin Li, Zhengli Xing

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We consider the problem of robust compressed sensing where the objective is to recover a high-dimensional sparse signal from compressed measurements partially corrupted by outliers. A new sparse Bayesian learning method is developed for this purpose. The basic idea of the proposed method is to identify the outliers and exclude them from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator variables to indicate which observations are outliers. These indicator variables are assigned a beta-Bernoulli hierarchical prior such that their values are confined to be binary. In addition, a Gaussian-inverse Gamma prior is imposed on the sparse signal to promote sparsity. Based on this hierarchical prior model, we develop a variational Bayesian method to estimate the indicator variables as well as the sparse signal. Simulation results show that the proposed method achieves a substantial performance improvement over existing robust compressed sensing techniques.

Original languageEnglish
Pages (from-to)104-109
Number of pages6
JournalSignal Processing
Volume140
DOIs
StatePublished - Nov 2017

Keywords

  • Outlier detection
  • Robust Bayesian compressed sensing
  • Variational Bayesian inference

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