A Machine Learning Approch To Inverse Acoustic Scattering Problem

Inverse Scattering is widely used in rader,petroleum exploration and biomedical imaging.Related research of numerical solution methods has important academic significace and practical value.In this paper,we study a typical inverse Scattering problem from the perspective of numerical calculation:using the far-field data of acoustic waves to rebuilt the shape of the impenetrable obstacles.The solution to such problems often faces challenges such as non-linearity and ill-posedness.Lots of scholars have conducted research on the scattering theory of wave equations,and proposed a large number of effective calculation methods,such as optimization methods,iterative algorithms and sampling methods to solve these problems.These algorithms are essentially dependent on the physical and mathematical models of the scattering problem,which can be reduced to model-driven computing methods.In recent years,machine learning technology has gained more and more attention in many fields,such as natural language processing and computer vision.Different from the traditional model-driven algorithm,deep learning is a data-driven algorithm which has achieved great success in solving inverse problems in image processing and geophysics.However,as far as we know,there is no research in the classical inverse scattering problem of shape reconstruction by using deep learning method.Therefore,this paper is purpose to study the application of deep learning techniques to such inverse scattering problems.We discuss its feasibility through computational examples,and compare the reconstruction effects of deep learning techniques and traditional algorithms.Specifically,the content of this paper is arranged as follows:The first chapter summarizes some background knowledge related to this research topic,including the research background and significance of the subject,the research history and development status in this direction at home and abroad,and the specific research model of this paper.The second chapter gives a brief introduction to the preliminary knowledge needed to solve the forward and inverse scattering problems,including potential theory,integral equation method for solving forward problems,and classical numerical methods for solving inverse scatter problems.Then we briefly review the basic content of deep learning,including the basic principles of artificial neural networks,the specific implementation of backpropagation algorithms,and the parameters selection strategies in neural networks.The third chapter and the fourth chapter are the main research results of this paper.The fourth chapter considers the most critical components of the deep learning algorithm,namely the training data set and the neural network structure.We propose two construction methods of training data sets at first,then discuss the framework of the algorithm implementation,and finally verify the proposed training set is simple and effective by numerical examples.The fourth chapter through a large number of numerical simulation experiments,including the results of all data and data missing cases in inverse scattering,and the comparison between the deep learning algorithm and the Newton iterative method.It shows that the deep learning algorithm is an effective solution to the inverse scattering problem.In particular,for the case of partial observation data for a single incident wave,the deep learning algorithm has the advantage of surpassesing the model-driven algorithm in inversion accuracy.