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.