Numerical Solution Of An Inverse Diffraction Problem From The Phaseless Data

With the development of science and application, inverse problem hasbecome one of the fastest growing areas of applied mathematics. In real life, ithas a very wide range of applications, such as Life sciences, Materials science,Remote Sensing Technology, Signal(image)processing. Acoustic and electro-magnetic scattering problems have become an important branch of inverseproblem of mathematical physics, which has a wide range of applications inAcoustic, Medical CT, Archeology, Radar etc. In short, the direct problem ofthe so-called sound waves is under the incident and scattered area known con-ditions, to solve the corresponding Far-field pattern. Accordingly, the inversescattering problem is that the solution of the scattering equation to determinethe scattering region (such as the shape of the scattering body, etc). Withrespect to the positive acoustic and electromagnetic scattering problems, theinverse scattering problems have relatively short history of the development,and mature slowly. We process mainly the inverse scattering problem from thephaseless data in this paper.In this paper, we have discussions as following: In Chapter1: We intro-duce briefly to the knowledge of the inverse problems and ill-posed problems,as well as some definitions, background and applications of scattering problem.Then we account the work done in this paper. In Chapter2: We formulate themathematical model of the scattering problem in the three-dimensional space, and at the second part we give the solving method of the forward problem.We mainly use the complex of double trapezoid formula. At last we give twonumerical simulations(One is rectangular region and another is circular area).Furthermore, according to the results of numerical experiments illustrate thefeasibility of the described method. In Chapter3: we also propose the modelof the inverse scattering problem at first(the function f is a real-valued func-tion). According to the features for the solution of the scattering problem, wepresent the method which combine the projection method with the Newtoniteration method.Then, we also use the method of Tikhonov Regulation. Fur-thermore, we give the specific process of the above algorithm. And then, wegive numerical examples under the case of taking n=23. So we verify thefeasibility of the algorithm.