Generalized beta Bayesian compressive sensing model for signal reconstruction

A new model-based Bayesian Compressive Sensing (BCS) algorithm is proposed. The statistical structure of the underlying signal is modeled by a two-state signal/noise Hidden Markov Tree (HMT) in the complex wavelet transform domain. This model is based on the recently addressed generalized beta mixtures of Gaussian distribution. A closed-form solution is derived for model parameters via Variational Bayes (VB) inference procedure. Using simulation results, it is shown that the reconstruction error of the proposed algorithm is lower than that of all the related well-known algorithms. Also, its CPU time is in general lower than most investigated algorithms.