Bayesian Compressive Sensing Using Laplace Priors

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. We present two algorithms resulting from our model; one global optimization algorithm and one constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, both algorithms are fully-automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation and therefore no user-in...

• Type: Journal
• Year: 2010
• Where: TIP
• Authors: S. Derin Babacan, Rafael Molina, Aggelos K. Katsaggelos
• Keywords: Model, TIP 2010, Unknown Signal, Unknown Signal Coefficients