Compressed Sensing: Fast Bayesian Matching Pursuit

Here is another Bayesian approach to Compressed Sensing. In Fast Bayesian Matching Pursuit, Philip Schniter, Lee C. Potter, and Justin Ziniel tell us how to reconstruct signals using a greedy algorithm and bayesian techniques. The abstract reads:

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

Of note is this text in the conclusion:

Numerical experiments suggest that the estimates returned by FBMP outperform (in normalized MSE) those of other popular algorithms (e.g., SparseBayes, OMP, StOMP, GPSRBasic, BCS) by several dB in typical situations.

No code yet available.