Designing local orthogonal bases on finite groups II: Nonabelian case

We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This, in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considered the abelian groups of unitary transformations, while here we deal with nonabelian groups. As an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. Such bases are useful for building systems for evaluating image quality. © 2000 Birkhäuser Boston. All rights reserved.