On the Relation Between Sparse Sampling and Parametric Estimation

We consider the relationship between parameter estimation of an additive model and sparse inversion of an under-determined matrix (dictionary) in a linear system. The dictionary is constructed by sampling parameters of the additive model. Parameters and model order are estimated using regularized least-squares inversion. We investigate equi-spaced and Fisher information inspired parameter sampling methods for dictionary construction, and present an example quantifying parameter estimation error performance for the different sampling methods. These results indicate that estimation performance is degraded by sampling the parameter space either too finely or too coarsely.