Bayesian Compressive Sensing using Laplace Priors

TitleBayesian Compressive Sensing using Laplace Priors
Publication TypeJournal Article
Year of Publication2010
AuthorsBabacan, S. D., R. Molina, and A. K. Katsaggelos
JournalIEEE Transactions on Image Processing
Volume19
Pagination53-64
Date Published1/2010
Abstract

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 sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully-automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation and therefore no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. 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.

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