Estimation of the Discrete Spectrum of Relaxations for Electromagnetic Induction Responses Using $\ell_{p}$-Regularized Least Squares for $0 \leq p \leq 1$

The electromagnetic induction response of a target can be accurately modeled by a sum of real exponentials. 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 letter, we present a modified
$\ell_{p}$
-regularized least squares algorithm, for
$0 \leq p \leq 1$
, that eliminates the nonnegative constraint. An empirical method for choosing the regularization parameter is also studied. Using tests on synthetic data and laboratory measurements, the proposed method is shown to provide robust estimates of the model parameters in practice.