Bayesian sparse signal recovery based on log-Laplacian prior

Abstract

This paper proposes a Bayesian sparse signal recovery algorithm. To improve performance on sparse representation, the log-Laplacian distribution is first defined. With a narrow main lobe and high tail values, it is used as a prior of the sparse signal to model the sparse characteristic. Note that analytical inference of the posterior of the sparse signal is a challenge, because the proposed log-Laplacian prior is not conjugate to the Gaussian likelihood. A maximum a posterior (MAP) estimation-based sparse signal recovery algorithm is further proposed. During the reconstruction of the sparse signal, MAP and maximum likelihood estimation are utilized to estimate the scaling parameter and noise variance, respectively, so as to avoid manual tuning of parameters. Additionally, with the use of the conjugate-gradient algorithm, large matrix inversion is avoided and computational efficiency is improved. Experimental results based on both simulated and measured data validate the effectiveness of the proposed log-Laplacian prior-based sparse signal recovery algorithm. Further, it is applied to micromotion parameters estimation and inverse synthetic aperture radar imaging to confirm its validity.