Robust Bayesian Compressed sensing
This work addresses the problem of robust signal recovery in compressed sensing for applications like imaging or communications, though it appears incremental as it builds on prior Bayesian methods.
The paper tackles robust compressed sensing by recovering sparse signals from measurements with outliers, developing a new sparse Bayesian learning method that identifies and removes outliers using binary indicator hyperparameters and a variational Bayesian approach, achieving substantial performance improvement over existing techniques.
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the outliers from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator hyperparameters to indicate which observations are outliers. These indicator hyperparameters are treated as random variables and assigned a beta process 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 hyperparameters as well as the sparse signal. Simulation results show that the proposed method achieves a substantial performance improvement over existing robust compressed sensing techniques.