TY - JOUR
T1 - Robust Bayesian compressed sensing with outliers
AU - Wan, Qian
AU - Duan, Huiping
AU - Fang, Jun
AU - Li, Hongbin
AU - Xing, Zhengli
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/11
Y1 - 2017/11
N2 - 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.
AB - 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.
KW - Outlier detection
KW - Robust Bayesian compressed sensing
KW - Variational Bayesian inference
UR - http://www.scopus.com/inward/record.url?scp=85019568019&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019568019&partnerID=8YFLogxK
U2 - 10.1016/j.sigpro.2017.05.017
DO - 10.1016/j.sigpro.2017.05.017
M3 - Article
AN - SCOPUS:85019568019
SN - 0165-1684
VL - 140
SP - 104
EP - 109
JO - Signal Processing
JF - Signal Processing
ER -