Bayesian compressed sensing using generalized Cauchy priors

Compressed sensing shows that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Noting that sparse signals can be well modeled by algebraic-tailed impulsive distributions, in this paper, we formulate the sparse recovery problem in a Bayesian framework using algebraic-tailed priors from the generalized Cauchy distribution (GCD) family for the signal coefficients. We develop an iterative reconstruction algorithm from this Bayesian formulation. Simulation results show that the proposed method requires fewer samples than most existing reconstruction methods to recover sparse signals, thereby validating the use of GCD priors for the sparse reconstruction problem.