  We propose a compressed sensing algorithm termed variance state propagation
(VSP) for block-sparse signals, i.e., sparse signals that have nonzero
coefficients occurring in clusters. The VSP algorithm is developed under the
Bayesian framework. A hierarchical Gaussian prior is introduced to depict the
clustered patterns in the sparse signal. Markov random field (MRF) is
introduced to characterize the state of the variances of the Gaussian priors.
Such a hierarchical prior has the potential to encourage clustered patterns and
suppress isolated coefficients whose patterns are different from their
respective neighbors. The core idea of our algorithm is to iteratively update
the variances in the prior Gaussian distribution. The message passing technique
is employed in the design of the algorithm. For messages that are difficult to
calculate, we correspondingly design reasonable methods to achieve approximate
calculations. The hyperparameters can be updated within the iteration process.
Simulation results demonstrate that the VSP algorithm is able to handle a
variety of block-sparse signal recovery tasks and presents a significant
advantage over the existing methods.
