Research On Multiple Obstacle Inverse Scattering Problem Based On Bayesian Method

Inverse obstacle scattering in medium is a kind of problem that has received widespread attention.This kind of inverse scattering problem has important practical significance in radar scanning,medical imaging,and stealth technology.In addition,when solving the problem of inverse obstacle scattering with medium,we often encounter the problem of missing data.Relevant research shows that machine learning method can compensate for the impact of missing data to a certain extent.Therefore,this paper is based on Bayesian method,solve complex scatters inverse problem in different medium.The main research contents and results of this paper include:1)Aiming at the problem of acoustic wave obstacle scattering in two-dimensional homogeneous medium,a Bayesian method for reconstructing single or multiple impenetrable obstacles is proposed.The position information of the impenetrable obstacles is taken as the prior information of the Bayesian method,and the shape of single or multiple impenetrable obstacles is reconstructed using Markov chain Monte Carlo(MCMC)algorithm.The results of numerical experiments show that this method can effectively reconstruct the shape of single or multiple obstacles in homogeneous medium.2)Aiming at the problem of acoustic wave obstacle scattering in two-dimensional inhomogeneous medium,a hybrid method for reconstructing single or multiple impenetrable obstacles is proposed under the condition that the refractive index is a binary function.Firstly,neural network is used to predict the number of obstacles in the medium.Then,the predicted number of obstacles is used as the prior information of Bayesian method.Finally,the MCMC algorithm is used to reconstruct the shape and position parameters of multiple obstacles.The results of numerical experiments show that this method can effectively reconstruct the number,shape and position of obstacles in inhomogeneous medium.3)Aiming at the problem of acoustic wave mixed obstacle scattering in a two-dimensional inhomogeneous medium,under the condition that the refractive index of the inhomogeneous medium is a binary function,considering several cracks and impenetrable obstacles buried in the medium,a Bayesian method for simultaneously reconstructing cracks and impenetrable obstacles is proposed.The position information of the mixed barrier is taken as the prior information of the Bayesian method,MCMC algorithm is used to reconstruct the shape parameters of cracks and impenetrable obstacles.The results of numerical experiments show that this method can effectively reconstruct the shape of mixed obstacles in inhomogeneous medium.In this paper,finite aperture data and full aperture data are considered when solving the inverse scattering problem.Numerical experiments show that Bayesian method reduces the impact of data missing to some extent.