  We consider the problem of recovering two-dimensional (2-D) block-sparse
signals with \emph{unknown} cluster patterns. Two-dimensional block-sparse
patterns arise naturally in many practical applications such as foreground
detection and inverse synthetic aperture radar imaging. To exploit the
block-sparse structure, we introduce a 2-D pattern-coupled hierarchical
Gaussian prior model to characterize the statistical pattern dependencies among
neighboring coefficients. Unlike the conventional hierarchical Gaussian prior
model where each coefficient is associated independently with a unique
hyperparameter, the pattern-coupled prior for each coefficient not only
involves its own hyperparameter, but also its immediate neighboring
hyperparameters. Thus the sparsity patterns of neighboring coefficients are
related to each other and the hierarchical model has the potential to encourage
2-D structured-sparse solutions. An expectation-maximization (EM) strategy is
employed to obtain the maximum a posterior (MAP) estimate of the
hyperparameters, along with the posterior distribution of the sparse signal. In
addition, the generalized approximate message passing (GAMP) algorithm is
embedded into the EM framework to efficiently compute an approximation of the
posterior distribution of hidden variables, which results in a significant
reduction in computational complexity. Numerical results are provided to
illustrate the effectiveness of the proposed algorithm.
