Quasi-newton Iteration Method For Reconstructing The Sound-soft Scatterer Base On Decomposition Model

Inverse problems have very broad application prospects,widely appear in variousfields of the natural sciences and practical engineering and technology, such as sub-surface prospecting, nondestructive material testing, medical CT, seismology, sonar andso on.The main difculty of inverse problems comes from their ill-posedness, namely,thesolution does not depend continuously on the input date. The inverse acoustic scatteringproblem is an important branch of the research of the inverse problems§it not onlyhave the common property of ill-posedness in the inverse problem, but also possess thenonlinear property of itself. In this paper, we mainly study the two dimension inverseproblem of reconstructing the impenetrable sound-soft scatterer, in other words, wemainly study the algorithm of reconstructing boundary from the far field pattern of thescattered wave. The major content and achievements of this issue as follows:The second chapter, we mainly introduce the direct problem which hold the Dirich-let boundary condition of sound-soft scatterer. At the same time, We expressed thediscretization methods of solving the direct problem which based on the simple layerpotential and double layer potential of the integral equation under the parameterizationof the scattered boundary. The third chapter, we propound the quasi-Newton algorithm which using the farfield pattern of the scattered wave to reconstruct the sound-soft scatterer, the algorithmis based on the simple layer potential and double layer potential under the decompositionmodel algorithm. The basic idea about the algorithm is that, established the nonlin-ear operator which from one boundary map to the the full field boundary,and then,solve the nonlinear equation by quasi-Newton method. In the iteration process of thealgorithm,the inverse scattering problem is decomposed a linear ill-posed problem and anonlinear problem. And we use the Tikhonov regularization method solve the ill-posedproblem. In the Tikhonov regularization method, we import the model function methodwhich based on the Morozov deviation principle to obtain the regularization parameter.Further, we notice the superimposition property of the incident wave for the far fieldpattern, then we propound the quasi-Newton algorithm which based on the decompo-sition model for the more incident waves, that promote efciency of the reconstructionalgorithm.In the forth chapter, for the diferent scatterers, we give the numerical simulationresult of the algorithm which we have ofered. In the fifth chapter, we summarize themainly results and the mainly existing problems of this paper, and illustrate its startingpoint. Last,we make a study for the future work.