Variational Bayesian Approach with a heavy-tailed prior distribution for solving a non-linear inverse scattering problem

21/09/2014
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Publication MaxEnt 2014
OAI : oai:www.see.asso.fr:9603:11334
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Variational Bayesian Approach with a heavy-tailed prior distribution for solving a non-linear inverse scattering problem

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Variational Bayesian Approach with a heavy-tailed prior distribution for solving a non-linear inverse scattering problem L. Gharsalli1, H. Ayasso2, B. Duchˆene1 and A. Mohammad-Djafari1 (1) Laboratoire des Signaux et Syst`emes (L2S), (UMR8506: CNRS - SUPELEC - Univ Paris-Sud), 3 rue Joliot-Curie, 91190 Gif-sur-Yvette, France (2) GIPSA-LAB, D´epartement Image Signal, (UMR5216: CNRS - Grenoble-INP Univ Joseph Fourier - Univ Stendhal), BP 46 - 38402, Saint Martin d’H`eres, France e-mail: Leila.GHARSALLI@lss.supelec.fr, Hacheme.Ayasso@gipsa-lab.grenoble-inp.fr, Bernard.Duchene@lss.supelec.fr, Ali.Mohammad-Djafari@lss.supelec.fr Abstract We consider a nonlinear inverse scattering problem where the goal is to recon- struct an image of an unknown object from measurements of the scattered field that results from its interaction with a known wave in the microwave frequency range. The forward modeling of the wave-object interaction is tackled through a domain integral representation of the electric field in a 2D-TM configuration. The inverse problem is solved in a Bayesian framework where the prior information is introduced via a heavy-tailed distribution [1] as sparse prior information. In fact, the sought object or the image to be reconstructed is supposed to be composed of homogeneous areas. This implies that the image gradient must be sparse. A Varia- tional Bayesian Approximation (VBA) technique [2] is then applied to compute the posterior estimators and reconstruct the object. References: [1] A. Mohammad-Djafari: Bayesian approach with prior models which enforce sparsity in signal and image processing. EURASIP journal on Ad- vances in Signal processing 2012, Special issue on Sparse Signal processing. [2] V. Sm´ıdl, A. Quinn: The Variational Bayes Method in Signal Processing (Signals and Communication technology). Secausus, NJ, USA: Springer-Verlag New York, Inc. 2006. Key Words: Inverse scattering, heavy tailed distribution, sparse prior, Variational Bayesian Approximation.