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Fast Bayesian compressive sensing using Laplace priors

By S. Derin Babacan, Rafael Molina and Aggelos K. Katsaggelos


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 parameters are estimated solely from the observation and therefore no user-intervention is needed. We provide experimental results with synthetic 1D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach. Index Terms — Bayesian methods, compressive sensing, inverse problems, sparse Bayesian learning, relevance vector machin

Topics: RVM
Year: 2009
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