We consider the problem of recovering 2D block-sparse signals with unknown cluster patterns. The 2D block-sparse patterns arise naturally in many practical applications, such as foreground detection and inverse synthetic aperture radar imaging. To exploit the underlying block-sparse structure, we propose a 2D pattern-coupled hierarchical Gaussian prior model. The proposed pattern-coupled hierarchical Gaussian prior model imposes a soft coupling mechanism among neighboring coefficients through their shared hyperparameters. This coupling mechanism enables effective and automatic learning of the underlying irregular cluster patterns, without requiring any a priori knowledge of the block partition of sparse signals. We develop a computationally efficient Bayesian inference method, which integrates the generalized approximate message passing technique with the proposed prior model. Simulation results show that the proposed method offers competitive recovery performance for a range of 2D sparse signal recovery and image processing applications over the existing method, meanwhile achieving a significant reduction in the computational complexity.
We propose a pattern-coupled sparse Bayesian learning method for inverse synthetic aperture radar (ISAR) imaging by exploiting a block-sparse structure inherent in ISAR target images. A two-dimensional pattern-coupled hierarchical Gaussian prior is proposed to model the pattern dependencies among neighboring scatterers on the target scene. An expectation-maximization (EM) algorithm is developed to infer the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.Index Terms-Block-sparse structure, expectation-maximization (EM), ISAR, pattern-coupled sparse bayesian learning.1070-9908
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