Bayesian sparse signal recovery based on log-Laplacian prior

Ting Gong; Shuanghui Zhang; Xiang Li

doi:10.1117/1.JRS.12.045003

10 October 2018 Bayesian sparse signal recovery based on log-Laplacian prior

Ting Gong, Shuanghui Zhang, Xiang Li

Author Affiliations +

Journal of Applied Remote Sensing, Vol. 12, Issue 4, 045003 (October 2018). https://doi.org/10.1117/1.JRS.12.045003

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.

Citation Download Citation

Ting Gong, Shuanghui Zhang, and Xiang Li "Bayesian sparse signal recovery based on log-Laplacian prior," Journal of Applied Remote Sensing 12(4), 045003 (10 October 2018). https://doi.org/10.1117/1.JRS.12.045003

Received: 7 June 2018; Accepted: 18 September 2018; Published: 10 October 2018

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KEYWORDS

Signal to noise ratio

Lithium

Space based lasers

Interference (communication)

Reconstruction algorithms

Radar

Computer simulations

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