Two-Dimensional Wreath Product Group-Based Image Processing
R. Foote, G. Mirchandani, D. Rockmore
Journal of Symbolic Computation, Special Issue on Computer Algebra and Signal Processing, 2004
Paper (pdf) / Paper (ps)
In previous work we established a general finite group-based
approach to signal and image processing, with special
attention to the use of certain wreath product groups for
image processing. We now complement and extend that to
two-dimensional (2-D) group-based theory.
We define the concepts of decomposable, separable, and
inseparable transforms. In particular, we construct a 2-D separable
wreath product transform (WPT). This also generalizes the familiar
2-D DFT and 2-D Haar transforms. This has a concomitant
multiresolution spectral transform via a multichannel
pyramid-structured filter bank. We describe a 2-D quadtree scanning
scheme and compare this separable 2-D WPT with the 1-D WPT.