We describe the general finite field wavelet transform, which operates on vectors of length pk for p a prime, k >= 0. This transform allows one to choose not only the analyzing wavelet, but the wavelet `machine' by which a tight frame is produced from the analyzing wavelet. We discuss an implementation of the transform, which uses an algorithm that reveals the multiresolution character of the transform. Finally, its applications to denoising and cryptography are discussed.
Carolyn Pfeffer Johnston,
"Wavelets defined over finite fields and the discrete wavelet transform", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205450; https://doi.org/10.1117/12.205450