In the work, we describe a method for constructing non- separable multidimensional folding operators and discuss preliminary obtained with a discrete rhomboidal local cosine transform. Our construction extends related work by Xia and Suter and Bernardini and Kovacevic by generalizing the definition of folding operators to include the use of non- abelian symmetry groups. A family of prototypical dihedral folding operators allows one to decompose L²(R²) into n subspaces supported on approximate equiangular sectors. We draw directly on the representation theory of finite groups, making use of the group algebra structure. The folding operators do not incorporate windows. Instead, the folding operators are constructed directly by using elements of the matrix group SO(2n).

Date Published: 4 December 2000
PDF: 12 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408637

Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)