Sparse Bayesian Learning with joint noise robustness and signal sparsity

Abstract

This study concerns the issue of jointly enhancing noise robustness and promoting signal sparsity in Sparse Bayesian Learning (SBL), which aims at addressing the performance deficiency of sparse signal recovery due to uninformative data with low signal-to-noise ratios. In particular, the authors propose a hierarchical prior noise model with a signal-dependent parametrisation and incorporate it into developing the robust SBL algorithms for sparse signal recovery. The main contribution of the proposed approach is twofold. The first is the new consideration of noise-robustness enhancement in building SBL algorithms, which devotes to noise awareness in counteracting outliers in measurements. Specifically, the idea of signal-sparsity enforcing is extended to build a Least Absolute Deviation like loss criterion with the proposed hierarchical prior model of measurement noise. The second is the novelty of using the signal-dependent parametrisation in the proposed noise model. Indeed, the signal-dependent mechanism plays an indispensable role in producing the reliable noise parameter estimation jointly with updating signal model parameters under the fast SBL framework. In addition to numerical simulation studies, the real-life application of radio tomographic imaging is presented to validate the proposed approach.