Estimation and application of discrete spectrum of relaxations for electromagnetic induction responses

The EMI 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. In this paper, a constrained linear method for estimating the parameters is formulated by enumerating the relaxation parameter space and imposing a nonnegative constraint on the parameters. 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. The estimated parameters are then used to cluster different targets types for classification.