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The paper presents a versatile library of analytic and quasi-analyticcomplex-valued wavelet packets (WPs) which originate from discrete splines ofarbitrary orders. The real parts of the quasi-analytic WPs are the regularspline-based orthonormal WPs designed in [2]. The imaginary parts are theso-called complementary orthonormal WPs, which, unlike the symmetric regularWPs, they are antisymmetric. Tensor products of 1D quasi-analytic WPs provide adiversity of 2D WPs oriented in multiple directions. For example, a set of thefourth-level WPs comprises 62 different directions. The designed computationalscheme in the paper enables us to get fast and easy implementation of the WPtransforms. The presented WPs proved to be efficient in signal/image processingapplications such as restoration of images degraded by either additive noise ormissing of up to 90% of their pixels.

Analytic and directional wavelet packets in the space of periodic signals