We consider the problem of recovering two-dimensional (2-D) block-sparsesignals with \emph{unknown} cluster patterns. Two-dimensional block-sparsepatterns arise naturally in many practical applications such as foregrounddetection and inverse synthetic aperture radar imaging. To exploit theblock-sparse structure, we introduce a 2-D pattern-coupled hierarchicalGaussian prior model to characterize the statistical pattern dependencies amongneighboring coefficients. Unlike the conventional hierarchical Gaussian priormodel where each coefficient is associated independently with a uniquehyperparameter, the pattern-coupled prior for each coefficient not onlyinvolves its own hyperparameter, but also its immediate neighboringhyperparameters. Thus the sparsity patterns of neighboring coefficients arerelated to each other and the hierarchical model has the potential to encourage2-D structured-sparse solutions. An expectation-maximization (EM) strategy isemployed to obtain the maximum a posterior (MAP) estimate of thehyperparameters, along with the posterior distribution of the sparse signal. Inaddition, the generalized approximate message passing (GAMP) algorithm isembedded into the EM framework to efficiently compute an approximation of theposterior distribution of hidden variables, which results in a significantreduction in computational complexity. Numerical results are provided toillustrate the effectiveness of the proposed algorithm.
展开▼
