Bayesian Approach to Inverse Acoustic Scattering from Disks and Line Cracks with Phaseless Data
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This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks and line cracks through properly chosen incoming waves in two dimensions. Given the Gaussian prior measure, the well-posedness of the posterior measure in the Bayesian approach is discussed. The Markov Chain Monte Carlo (MCMC) method is adopted in the numerical approximation and the preconditioned Crank-Nicolson (pCN) algorithm with random proposal variance is utilized to improve the convergence rate. Numerical examples are provided to illustrate effectiveness of the proposed method.
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