Date of Award

Spring 2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Songming Hou

Abstract

This dissertation presents a novel method for the inverse scattering problem for extended target. The acoustic or electromagnetic wave is scattered by the target and received by all the transducers around the target. The scattered field on all the transducers forms the response matrix which contains the information of the geometry of the target. The objective of the inverse scattering problem is to reconstruct the shape of the scatter using the Response Matrix.

There are two types of numerical methods for solving the inverse problem: the direct imaging method and the iterative method. Two direct imaging methods, MUSIC method and Multi-tone method, are introduced in this dissertation. The direct imaging method generates the image, which contains the shape of the target, by defining the image function using the response matrix. Numerical examples show that the two direct imaging methods are efficient and robust, and the Multi-tone method can be used in synthetic aperture.

The iterative method described in this dissertation achieves better accuracy than the direct imaging method. The result of the direct imaging method of the inverse problem is used as an initial estimation for this iterative method. One forward problem and one adjoint problem is solved in each iteration step. Numerical results show that the residual vanishes at a fixed wave number. The final result after iterations is more accurate than the result from the direct imaging method.

This dissertation also introduces the application of the inverse problem: shape identification and classification. The response matrix used in shape classification can be generated by the forward solver or Born approximation. The distance function designed using a response matrix or its SVD information is effective and robust to noise. The classification method using the response matrix is tested on a large data set and compared with other classification algorithms on the retrieval accuracy.

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