Pattern-Coupled Sparse Bayesian Learning For Two-Dimensional Sparse Signal Recovery

This thesis aims at leveraging the block-sparse structure of the two-dimensional signals to enhance the sparse signal recovery performance. To this objective, we develop a two-dimensional pattern-coupled sparse Bayesian learning algorithm to capture the underlying cluster patterns of the signal. Furthermore, a generalized approximate message passing technique based algorithm is developed to reduce the computational complexity of the conventional sparse Bayesian learning method. Numerical results reveal that proposed method can reduce the computational complexity dramatically, meanwhile achieving a competitive recovery performance.We first propose a two-dimensional hierarchical Gaussian model to exploit the underlying cluster patterns of the signal. Based on this model, a pattern-coupled sparse Bayesian learning method is developed. An expectation-maximization (EM) technique is employed to infer the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. The proposed method is effective and flexible to exploit the underlying block-sparse structures, without requiring the prior knowledge of the block partition. Experimental results demonstrate that the proposed method is able to achieve a substantial performance improvement over existing algorithms, including the conventional SBL method.Then we consider the problem of how to reduce the computational complexity of the conventional sparse Bayesian learning methods. We develop a computationally efficient Bayesian inference method which integrates the generalized approximate message passing technique with the proposed prior model. The algorithm is also developed within the EM framework, using the generalized approximate message passing to efficiently compute approximations of the posterior distributions of the hidden variables. The hyperparameters associated with the hierarchical Gaussian prior are learned by iteratively maximizing the Q-function which is calculated based on the posterior approximations obtained from the generalized approximate message passing. Simulation results show that the proposed method offers competitive recovery performance for a range of two-dimensional sparse signal recovery and image processing applications over existing method, meanwhile achieving a significant reduction in computational complexity.