On the Optimality of Hermite Functions

Heisenberg Uncertainty Principle

This presentation is predicated on the following interpretation of Heisenberg's uncertainty principle:

A function can not be arbitrarily local in both the spatial and spatial frequency domains simultaneously.

The functions of interest are transform basis functions. We are primarily interested in local transforms; those from which the location and spectral content of an image event can be deduced with a high degree of certainty from the transform coefficients. We hope to achieve this locality by using basis functions which are themselves local in both the spatial and spatial frequency domains.