Fast bayesian compressive sensing using Laplace priors

  • Authors:

  • S. Derin Babacan;Rafael Molina;Aggelos K. Katsaggelos

  • Affiliations:

  • Department of Electrical Engineering, and Computer Science, Northwestern University, Evanston, IL 60208, USA;Departamento de Ciencias, de la Computación e I.A., Universidad de Granada, 18071, Spain;Department of Electrical Engineering, and Computer Science, Northwestern University, Evanston, IL 60208, USA

  • Venue:
  • ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
  • Year:
  • 2009

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Abstract

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.