SUPERVISORS: A Time Domain Formulation of Inverse Source Problems Using the Transmission-Line Matrix Method

The inverse source problem of electromagnetics for homogeneous background medium is investigated numerically using the Transmission-Line l\/Iatrix (TLM) method. By transforming all sources and fields into t heir equivalent link impulses inside a TLM computational domain, a discrete linear inversion formulation is developed. Our ap-proach solves for t he unknown source distribution inside a given source region using t he near-field measurements on its boundary. Unlike t he conventional frequency-domain t reatments, both our source solut ion and the field measurements are obtained in t he t ime domain. The non-uniqueness of the inverse source problem is addressed by addi t ionally imposing a smoothness prior constraint. First-order t ime and spa-t ial derivatives of t he source distribut ion are minimized. The source reconstruction algorithm int roduced in this t hesis is illustrated through various two-dimensional nu-merical examples. It is also shown that our algorit hm is robust against t he noise from the boundary field measurements. II