Open AccessTree‐structured Bayesian compressive sensing via generalised inverse Gaussian distribution
Author(s) -
Wang Maojiao,
He Xiaohai,
Qing Linbo,
Xiong Shuhua
Publication year - 2017
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2016.0408
Subject(s) - compressed sensing , underdetermined system , algorithm , bayesian probability , computer science , inverse problem , posterior probability , wavelet , prior probability , bayesian inference , gaussian , context (archaeology) , sampling (signal processing) , mathematics , artificial intelligence , computer vision , mathematical analysis , paleontology , physics , filter (signal processing) , quantum mechanics , biology
Compressive sensing (CS) implements signal sampling and compression simultaneously, which significantly alleviates the pressure on the sampling end. However, the reconstruction algorithm is an underdetermined linear inverse problem. To solve this problem, it is crucial to involve prior knowledge regarding the reconstructed signal. In this study, the compressibility of wavelet coefficients is utilised as prior knowledge. Moreover, a generalised inverse Gaussian (GIG) distribution is integrated in the context of tree‐structured Bayesian CS (TSBCS), which also imposes the persistence property between the successive levels. Finally, variational Bayesian inference is used to infer the posterior probability distribution of the model parameters. Due to the overall algorithm is based on TSBCS, the proposal is referred to as TSBCS via a GIG distribution (TSBCS‐GIG). Experimental results show that the authors’ proposed TSBCS‐GIG algorithm outperforms other well‐known algorithms in both peak signal‐to‐noise ratio and visual quality.