Fast bayesian matching pursuit

A low-complexity recursive procedure is presented for minimum mean squared error (MMSE) estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both an approximate MMSE estimate of the parameter vector and a set of high posterior probability mixing parameters. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and MAP model selection. The set of high probability mixing parameters not only provides MAP basis selection, but also yields relative probabilities that reveal potential ambiguity in the sparse model.