Improving spectral resolution using basis selection

In this paper, we develop high resolution nonparametric spectrum estimation methods using basis selection methodology. As opposed to standard minimisation of the l₂ norm of the solution, it is shown that by minimizing suitable diversity measures associated with the linear representation problem one can obtain high resolution spectrum estimates. Algorithms for this purpose are discussed with attention being paid to the robustness issue. In particular, methods are developed to accommodate noise in measurements using a Bayesian framework, and to incorporate statistical averaging using a novel multiple measurement vector framework