| Inverse scattering problem arise when we illuminate a medium with (acoustic, electromagnetic, elastic) energy, observe the scattered field, and from these infer the contents of the medium. It has applications in numerous fields, like non-destructive testing, the imaging of earths interior, oil prospecting, medical imaging, fault detection for undersea cables and transmission lines, etc..;The inverse scattering problem was considered highly ill-posed, till Chen and Rokhlin came up with a stable algorithm in one dimension. In this dissertation we consider how to recover the parameters of a LC ladder network from its input admittance, using Chen-Rokhlin like algorithms. In contrast to conventional wisdom, which holds that these parameters cannot be recovered accurately, we show that inclusion of a single negative resistor, along with the use of the right algorithms, can enable us to recover these parameters accurately. These ideas can be used to construct wired sensor networks. |
