Discrete rotation for directional orthogonal wavelet packets

We propose a simple and new way of defining the directional wavelet packets basis. This new decomposition is based on a discrete rotation. To avoid information loss or modification (in order to keep the orthogonality property) we use a new one-to-one discrete rotation. This rotation is based on three discrete shear transformations. This new oriented basis does not divide the 2D Fourier plane into square regions. Instead of horizontal and vertical favourite directions, our directional scheme treats different arbitrary directions