Image reconstruction from compressive samples via a max-product EM algorithm

摘要

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing structured approximatelysparse signals via belief propagation. The measurements follow an underdetermined linear model where theregression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussiannoise with an unknown variance. The signal is composed of large- and small-magnitude components identifiedby binary state variables whose probabilistic dependence structure is described by a hidden Markov tree (HMT).Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys’ noninformativeprior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aimsat maximizing the posterior distribution of the signal and its state variables given the noise variance. We employa max-product algorithm to implement the maximization (M) step of our EM iteration. The noise variance isa regularization parameter that controls signal sparsity. We select the noise variance so that the correspondingestimated signal and state variables (obtained upon convergence of the EM iteration) have the largest marginalposterior distribution. Our numerical examples show that the proposed algorithm achieves better reconstructionperformance compared with the state-of-the-art methods.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.