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, line cracks and kite-shaped obstacles 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.

中文翻译：

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使用无相远场数据进行反时谐声波散射的贝叶斯方法

本文涉及从无相远场数据推断声软障碍物的位置和形状的逆声散射问题。我们提出了贝叶斯方法，通过正确选择的二维入射波来恢复声音软盘、线裂缝和风筝形障碍物。给定高斯先验测度，讨论了贝叶斯方法中后验测度的适定性。数值逼近采用马尔可夫链蒙特卡罗(MCMC)方法，并利用随机提议方差的预处理Crank-Nicolson(pCN)算法提高收敛速度。提供了数值例子来说明所提出方法的有效性。