Application of ℓp-regularized least squares for 0 ≤ p ≤ 1 in estimating discrete spectrum models from sparse frequency measurements

It is difficult to robustly estimate the parameters of an additive exponential model from a small number of frequency-domain measurements, especially when the model order is unknown and the parameters must be constrained to be real. Recent work in sparse sampling and sparse reconstruction casts this problem as a linear dictionary selection problem by densely sampling the parameter space. We present a modified ℓp-regularized least squares algorithm, for 0 ≤ p ≤ 1, and show that it is effective when the frequency sampling is sparse over a couple of decades and the parameters must be estimated over more than four decades. An empirical method for choosing the regularization parameter is also studied. Using tests on synthetic data and laboratory measurements for an EMI application, the proposed method is shown to provide robust estimates of the model parameters up to eighth order.