Bayesian Compressive Sensing using Laplace Priors
D. Babacan, M. Luessi, R. Molina, and A.K. Katsaggelos, “Bayesian Compressive Sensing Using Laplace Priors”, IEEE Transaction on Image Processing, vol. 19, no. 1, 53-63, 2010. [BibTeX entry][Abstract][ (1919 KB.)]
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 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 1-D signals and images, and compare with the state-ofthe-art CS reconstruction algorithms demonstrating the superior
performance of the proposed approach.
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