Detecting Line Sources inside Cylinders by Analytical Algorithms

Abstract

Inverse problems for line sources radiating inside a homogeneous magneto-dielectric cylinder are investigated. The developed algorithms concern the determination of the location and the current of each source. These algorithms are mostly analytical and are based on proper exploitation of the moments obtained by integrating the product of the total field on the cylindrical boundary with complex exponential functions. The information on the unknown parameters of the problem is encoded in these moments, and hence all parameters can be recovered by means of relatively simple explicit expressions. The cases of one and two sources are considered and analyzed. Under certain conditions, the permittivity and permeability of the cylinder are also recovered. The results from two types of numerical experiments are presented: (i) for a single source, the effect of noise on the boundary data is studied, (ii) for two sources, the pertinent nonlinear system of equations is solved numerically and the accuracy of the derived solution is discussed.