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In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in...
In this paper, we propose a novel algorithm for image reconstruction from compressive measurements of wavelet coefficients. By incorporating independent Laplace priors on separate wavelet sub-bands, the inhomogeneity of wavelet coefficient distributions and therefore the structural sparsity within images are modeled effectively. We model the problem by adopting a Bayesian formulation, and develop...
In this paper we model the components of the compressive sensing (CS) problem using the Bayesian framework by utilizing a hierarchical form of the Laplace prior to model sparsity of the unknown signal. This signal prior includes some of the existing models as special cases and achieves a high degree of sparsity. We develop a constructive (greedy) algorithm resulting from this formulation where necessary...
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