Analytic and directional wavelet packets

The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of quasi-analytic WPs are the regular spline-based orthonormal WPs designed in [1]. The imaginary parts are the so-called complementary orthonormal WPs, which, 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, the set of fourth-level WPs comprise 62 different directions. The designed computational scheme enables extremely fast and easy implementation of the WP transforms.