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The interior inverse scattering problem for a two-layered cavity using the Bayesian method

  • * Corresponding author: Weishi Yin

    * Corresponding author: Weishi Yin 
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  • In this paper, the Bayesian method is proposed for the interior inverse scattering problem to reconstruct the interface of a two-layered cavity. The scattered field is measured by the point sources located on a closed curve inside the interior interface. The well-posedness of the posterior distribution in the Bayesian framework is proved. The Markov Chain Monte Carlo algorithm is employed to explore the posterior density. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method.

    Mathematics Subject Classification: Primary: 78A46, 35R30, 65N21; Secondary: 62F15.

    Citation:

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  • Figure 1.  A schematic illustration of the two-layered cavity scattering problem

    Figure 2.  Recoveries of the circle-shaped interface $ \Gamma_{0} $ by the Bayesian method with $ \sigma = 0.005,0.01,0.05 $, respectively

    Figure 3.  The Markov chains of the coefficients $ q_{0},a_{1} $ and $ b_{1} $ with $ \sigma = 0.005,0.01,0.05 $, respectively

    Figure 4.  Recoveries of the peanut-shaped interface $ \Gamma_{0} $ by the Bayesian method with $ \sigma = 0.005,0.01,0.05 $, respectively

    Figure 5.  The Markov chains of the coefficients $ q_{0},a_{1} $ and $ b_{1} $ with $ \sigma = 0.005,0.01,0.05 $, respectively

    Figure 6.  Recoveries of the peanut-shaped interface $ \Gamma_{0} $ by the Bayesian method with $ \rho = 0.3,0.2,0.1 $, respectively

    Figure 7.  The Markov chains of the coefficients $ q_{0},a_{1} $ and $ b_{1} $ with $ \rho = 0.3,0.2,0.1 $, respectively

    Figure 8.  Recoveries of the peanut-shaped interface $ \Gamma_{0} $ by the Bayesian method with $ \gamma_{1},\gamma_{2} $ and $ \gamma_{3} $, respectively

    Figure 9.  The Markov chains of the coefficients $ q_{0},a_{1} $ and $ b_{1} $ with $ \gamma_{1},\gamma_{2} $ and $ \gamma_{3} $, respectively

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