  The paper presents a versatile library of quasi-analytic complex-valued
wavelet packets (WPs) which originate from polynomial splines of arbitrary
orders. The real parts of the quasi-analytic WPs are the regular spline-based
orthonormal WPs designed in [1]. The imaginary parts are the so-called
complementary orthonormal WPs that are derived from the Hilbert transforms of
the regular WPs and, unlike the symmetric regular WPs, are antisymmetric.
Tensor products of 1D quasi-analytic WPs provide a diversity of 2D WPs oriented
in multiple directions. For example, a set of the fourth-level WPs comprises 62
different directions. The properties of the presented WPs are refined frequency
resolution, directionality of waveforms with unlimited number of orientations,
(anti-)symmetry of waveforms and windowed oscillating structure of waveforms
with a variety of frequencies. Directional WPs have a strong potential to be
used in various image processing applications such as restoration of degraded
images and extraction of characteristic features from the images.
