Reconstruction of source distributions on a nonuniform LCRG line using an optimization approach

The reconstruction of spatial source distributions on a nonuniform LCRG line is considered in the time-domain. An optimization approach is used to reconstruct two source distribution functions (induced by electric and magnetic fields, respectively) using the received transient voltages at the two endpoints of the line. By introducing auxiliary functions, the gradient of the objective functional is found as an explicit expression. The two source distribution functions are then reconstructed simultaneously by an iterative algorithm (the conjugate gradient method). Numerical results show that the present algorithm for the reconstruction is robust, and stable under noise of the measured signals and any perturbation of the known parameters. Conditions for a reliable simultaneous reconstruction using only one-sided measurements are also discussed and tested numerically.