Date of Award

Fall 2021

Document Type


Degree Name

Master of Science (MS)


Electrical and Computer Engineering

First Advisor

Richie, James

Second Advisor

Lee, Chung Hoon

Third Advisor

Black, Jennifer


The linear sampling method (LSM) is a simple and effective qualitative method to reconstruct the support of unknown object by solving inverse scattering problem. The solution is done based on the field radiated by the elementary source located in a set of test points. In this thesis, the LSM formulation, limitations of standard LSM and extensions of LSM are discussed. Standard LSM can reconstruct simply connected objects, but it fails in case of concave or not simply connected objects. However, it can reconstruct the convex hull for such objects. Some extensions to LSM have been proposed to avoid these limitations. Two of these extensions are generalized LSM (GLSM) and multipole based LSM (MLSM). GLSM is formulated by generalizing the right side of the linear equation to higher order multipoles. This provides more information about the radiated field. The reconstruction is even better by using some post-processing scheme such as a modified indicator function and higher values for the regularization parameter. But GLSM cannot reconstruct the actual shape for some complex objects. MLSM is based on physical regularization. This method analyzes the multipole expansion of the scattered field. Only monopole and dipole terms are used for the reconstruction. This modification shows better reconstruction than the mathematical regularization in GLSM. Another advantage of MLSM is that the threshold for boundary contour is constant for all types of objects. From the results, it is evident that MLSM is somewhat better than GLSM when the object’s complex hull is very different than the object itself. However, higher permittivity affects the solutions. It can be avoided by using higher value of regularization parameter in GLSM but in MLSM there is no known remedy.

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