Detection issues over multiresolution subspaces

In this article we extend our earlier work and explore rigorously the environment supported by multiresolution subspaces. Specifically, we obtain the relationships between Karhunen-Loeve (KL) bases derived from the projections of signals onto subspaces and sums of subspaces; derive the detectability measures over subspaces and discuss detection strategies from the view point of maximizing detectability. The purpose of this paper is to establish the rules for optimal detection over multiresolution subspaces. It is expected that the theory developed will be useful in developing strategies for optimal and sub-optimal detectors.