Bayesian compressive sensing using tree-structured complex wavelet transform

Abstract

The tree-structured complex wavelet Bayesian compressing sensing (TSCW-BCS) is introduced. The Bessel K form (BKF) probability density function; which has heavy tails out of the origin, is used as the prior. The inter-scale statistical relation between complex wavelet coefficients is modelled by the hidden Markov tree. The Markov chain Monte Carlo inference is obtained based on the BKF and then the posterior parameters of wavelet coefficients are derived. Simulation results show that the proposed TSCW-BCS outperforms many well-known CS methods.