A fast BSBL algorithm has been derived, and the work has been submitted to IEEE Signal Processing Letters.
Below is the paper:
Fast Marginalized Block SBL Algorithm
by Benyuan Liu, Zhilin Zhang, Hongqi Fan, Zaiqi Lu, Qiang Fu
The preprint can be downloaded at: http://arxiv.org/abs/1211.4909
Here is the abstract:
The performance of sparse signal recovery can be improved if both sparsity and correlation structure of signals can be exploited. One typical correlation structure is intra-block correlation in block sparse signals. To exploit this structure, a framework, called block sparse Bayesian learning (BSBL) framework, has been proposed recently. Algorithms derived from this framework showed promising performance but their speed is not very fast, which limits their applications. This work derives an efficient algorithm from this framework, using a marginalized likelihood maximization method. Thus it can exploit block sparsity and intra-block correlation of signals. Compared to existing BSBL algorithms, it has close recovery performance to them, but has much faster speed. Therefore, it is more suitable for recovering large scale datasets.