Date of Award

Winter 2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Songming Hou

Abstract

The dissertation presents an improved method for the inverse scattering problem to obtain better numerical results. There are two main methods for solving the inverse problem: the direct imaging method and the iterative method. For the direct imaging method, we introduce the MUSIC (MUltiple SIgnal Classification) algorithm, the multi-tone method and the linear sampling method with different boundary conditions in different cases, which are the smooth case, the one corner case, and the multiple corners case. The dissertation introduces the relations between the far field data and the near field data.

When we use direct imaging methods for solving inverse scattering problems, we observe artificial lines which make it hard to determine the shape of targets. We try to eliminate those lines in different frequencies, but the artificial lines are still in the results and we are forced to get the shape of the targets. Hence, we try to apply multiple frequency data to obtain better results.

There are several reasons to cause the artificial lines. For example, the creation of the response matrix, the error of solving the forward problem and the error of the computation. We propose a signal space test to study the cause of the artificial lines and to use multiple frequency data to reduce the effect from them.

Finally, we use the active contour method to further improve the imaging results. This dissertation introduces the active contour method and the level-set algorithm. We use the results of the multiple frequencies to obtain the level-set data by utilizing the active contour method and the level-set algorithm. By using the level-set data, we reconstruct the shape of the targets without artificial lines. In order to demonstrate the robustness of the MUSIC algorithm, we add noise to the response matrix.

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