Robust Estimation of the Discrete Spectrum of Relaxations for Electromagnetic Induction Responses

The electromagnetic induction response of a target can be accurately modeled by a sum of real exponentials. However, it is difficult to obtain the model parameters from measurements when the number of exponentials in the sum is unknown or the terms are strongly correlated. Traditionally, the time constants and residues are estimated by nonlinear iterative search. In this paper, a constrained linear method of estimating the parameters is formulated by enumerating the relaxation parameter space and imposing a nonnegative constraint on the parameters. The resulting algorithm does not depend on a good initial guess to converge to a solution. By using tests on synthetic data and laboratory measurement of known targets, the proposed method is shown to provide accurate and stable estimates of the model parameters.