Fast Inverse-Free Generalized Sparse Bayesian Iearning Algorithm

Sparse Bayesian learning (SBL) has been a popular method for sparse signal recovery under the standard linear model (SLM). Since SBL involves a matrix inversion in each iteration, the computation complexity is usually very high when applied to problems with large data set. Consequently, an inversefree sparse Bayesian learning (IF-SBL) algorithm has been proposed to achieve lower reconstruction errors than other state-of-the-art fast sparse recovery methods in low signal-to-noise ratio (SNR) scenarios. In practice, many problems can be formulated as a generalized linear model (GLM) where measurements are obtained in a nonlinear way such as image classification and estimation from quantized data. This work develops inverse-free generalized sparse Bayesian learning (IF-Gr-SBL), which can be viewed as performing iterations between two modules, where one module performs the standard IF-SBL algorithm, the other module performs the minimum mean squared error (MMSE) estimation. Finally, numerical experiments show the effectiveness