In this paper, a novel model-based distributed compressive sensing (DCS) algorithm is proposed. DCS exploits the inter-signal correlations and has the capability to jointly recover multiple sparse signals. Proposed approach is a Bayesian decentralized algorithm which uses the type 1 joint sparsity model (JSM-1) and exploits the intra-signal correlations, as well as the inter-signal correlations. Compared to the conventional DCS algorithm, which only exploit the joint sparsity of the signals, the proposed approach takes the intra- and inter-scale dependencies among the wavelet coefficients into account to enable the utilization of the individual signal structure. Furthermore, the Bessel K-form (BKF) is used as the prior distribution which has a sharper peak at zero and heavier tails than the Gaussian distribution. The variational Bayesian (VB) inference is employed to perform the posterior distributions and acquire a closed-form solution for model parameters. Simulation results demonstrate that the proposed algorithm have good recovery performance in comparison with state-of the-art techniques.

本文提出了一种新颖的基于模型的分布式压缩感知（DCS）算法。DCS利用信号间相关性，并具有共同恢复多个稀疏信号的能力。提出的方法是一种贝叶斯分散算法，该算法使用类型1联合稀疏模型​​（JSM-1）并利用信号内相关以及信号间相关。与仅利用信号的联合稀疏性的常规DCS算法相比，所提出的方法考虑了小波系数之间的尺度内和尺度间相关性，从而能够利用单个信号结构。此外，贝塞尔K型（BKF）用作先验分布，与0的高斯分布相比，其零位处的峰更尖且尾部更重。使用变分贝叶斯（VB）推断来执行后验分布并获取模型参数的封闭形式解。仿真结果表明，与最新技术相比，该算法具有良好的恢复性能。