A Linear Sampling multiple frequency method for target detection

In the field of inverse scattering problems of electromagnetic imaging, there are many techniques that can be used to detect unknown objects. Generally these methods maintain a direct relationship between the precision of the target shape and the amount of time required to obtain the solution. However, it has been shown that hybridization, or a combination of techniques, can be used to obtain the shape reconstruction that is accurate and less expensive computationally. Previous research in the Computational Electromagnetics Group of Professor El-Shenawee at the University of Arkansas has looked into the use of hybridization by combining the Level Set algorithm, a precise but slow shape reconstruction technique, with the Linear Sampling Method (LSM), a very fast technique. It was found that taking the result from the LSM and using it as the initial guess of the Level Set algorithm can enhance the computational expenses. The goal of this work is to implement a multiple frequency model of the LSM and to test it for two-dimensional metallic targets. The results show that a reasonably accurate reconstruction could be attained using the multiple frequency LSM technique to detect single and multiple targets. The results also show that some frequencies, not know a priori, can deteriorate the detection of the target. However, averaging the detected targets over a band of frequencies has shown a potential of more accurate results compared to the use of a single frequency. This work focused on the microwave band of frequency; however, the preliminary results will be extended to the terahertz band

Utilizing higher-order basis functions for estimating the shape of metallic and dielectric objects

Представљена је квалитативна метода нумеричке електромагнетике за микроталасно формирање слике, која се ослања на решавање инверзног проблема расејања. У уводном делу дат је преглед литературе и укратко су дефинисане предности предложеног алгоритма у односу на већ постојеће методе. Након увода, дефинисани су основни постулати инверзних проблема и упоређени са добро познатом формулацијом директних електромагнетских проблема. Након тога, објашњене су потешкоће које настају при решавању инверзних проблема, односно показано је да су они у општем случају нелинеарни и некоректно постављени. Такође, детаљно је описана техника развоја по мултиполима као фундаментална алатка у аналитичкој електромагнетици, на којој се заснива приказана метода...An electromagnetic qualitative microwave imaging method, which relies on solving an inverse scattering problem, is presented. In the introductory part of this dissertation, the state-of-the-art is briefly summarized. Also, main advantages of the proposed method, compared to other known methods, are outlined. After the introduction, we define the basic idea of an inverse problem, compared to the well-known direct electromagnetic problem formulation. Then, we explain the main difficulties arising during an attempt to solve such an inverse problem, i.e., it is shown that these problems are generally non-linear and ill-posed. Also, the multipole expansion technique, as a fundamental tool in analytical electromagnetics, is described in detail..