Directional wavelet packets originating from polynomial splines

The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines arbitrary orders. Discrete Fourier transforms (DFT) qWPs are located in either positive or negative half-band the frequency domain. Consequently, DFTs 2D qWPs, derived by tensor products 1D occupy one quadrants Such structure DFT spectra results directionality their real parts. Due to fact that well localized domain, shapes parts close windowed cosine waves oscillating variety different directions with frequencies. For example, set fourth-level comprises 314 and 256 above properties combined fast transform implementation make directional strong tool for application image processing tasks such as restoration degraded images extraction characteristic features use them deep learning. A few illustrations successful designed denoising, inpainting, classification given paper.