  This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA)
for reconstructing block-sparse signals with unknown block structures. Unlike
the existing algorithms for block sparse signal recovery which assume the
cluster structure of the nonzero elements of the unknown signal to be
independent and identically distributed (i.i.d.), we use a more realistic
Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d.
block-sparse signals commonly encountered in practice. The Block-IBA
iteratively estimates the amplitudes and positions of the block-sparse signal
using the steepest-ascent based Expectation-Maximization (EM), and optimally
selects the nonzero elements of the block-sparse signal by adaptive
thresholding. The global convergence of Block-IBA is analyzed and proved, and
the effectiveness of Block-IBA is demonstrated by numerical experiments and
simulations on synthetic and real-life data.
