Distribution agnostic Bayesian matching pursuit based on the exponential embedded family

Compressed sensing (CS) is an emerging field that allows to recover high-dimensional sparse signal from a few compressed measurements. Classical CS algorithms using the Bayesian framework generally impose a sparseness-promoting prior on the signal, which may not characterize the real signals with diversity. Moreover, estimating the parameters involved in the prior is challenging especially for non-i.i.d. signals. In this paper, we propose an efficient prior-agnostic Bayesian matching pursuit for sparse signal recovery, which avoids the risk of imposing mismatched prior on the signals and enjoys lower complexity than Bayesian approaches due to the elimination of prior parameter estimation. Specifically, we utilize the noise model and the reduced exponential embedded family (EEF) to obtain an approximate likelihood of interest, and then find the most dominant supports with maximum approximate likelihoods in a greedy manner to give an approximate minimum mean squared error (MMSE) estimate for the sparse signal. Experiment results demonstrate that our method achieves lower normalized mean squared error (NMSE) while higher efficiency compared to the state-of-the-art methods.