A Numerical Method For The Shape Reconstruction Of Sound-soft Obstacle Based On Phaseless Data

In this paper,we mainly consider the problem of the shape reconstruction of soundsoft 2-D obstacle based on phaseless far-field data.Many numerical algorithms may not be applied because of the lack of phase information from the measured far-field data.Referring to a class of nonlinear integral equation iteration method proposed by Johansson and Sleeman in [2],it is applied to the obstacle inverse scattering problems from phaseless far-field data.First,the boundary problem and the Huygens principle are used to transform the original problem into a set of boundary integral equations consisting of field equation and phaseless data equation;Secondly,an initial approximation is given to the boundary,finding the density function from the field equation,then the density function is replaced by the phaseless data equation.Linearize phaseless data equation about boundary parameter,calculating the far field operator of the Fr?echet derivative;Finally,using relaxed Newton method with Tikhonov regularization solution of the boundary value correction,so that each iteration step can get a new approximate boundary,and the feasibility of this method is illustrated by numerical experiments.On the basis of 2-D research results,we extend to the 3-D numerical method for the problems of Helmholtz equation.In theory,we give a fully discrete iterative scheme.