Application of ?_p-regularized Least Squares For 0 ≤ p ≤ 1 in Estimating Discrete Spectrum of Relaxations For Electromagnetic Induction Responses

摘要

Broadband EMI sensors have been shown to be capable of detecting and discriminating mines and subsurface explosive objects. It is advantageous to model the EMI frequency response of a target in terms of a discrete spectrum model (or equivalently a sum of real exponentials in the time domain) that is valuable in discrimination. However, in practice it is difficult to obtain the model parameters from measurements. We previously proposed a constrained linear method that can robustly estimate the model parameters when they are nonnegative. In this paper, we present a modified ?_p-regularized least squares algorithm, for 0 ≤ p ≤ 1, that eliminates the nonnegative constraint. Using synthesized data and lab measurements, the proposed spectrum estimation method is shown to be effective. The results suggest that the proposed method can be used to obtain spectrum of targets for discrimination. We also propose a regularization parameter selection rule for the ?_p minimization.