Robust Bayesian Compressed sensing

TL;DR

This paper introduces a novel Bayesian approach for robust compressed sensing that effectively identifies and removes outliers, leading to improved recovery of high-dimensional sparse signals from corrupted measurements.

Contribution

A new hierarchical Bayesian model with indicator hyperparameters and variational inference for robust sparse signal recovery from outlier-corrupted data.

Findings

Significant performance improvement over existing methods

Effective outlier detection and removal

Robust recovery of sparse signals

Abstract

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.