Directional wavelet packets originating from polynomial splines
| Autor: | Averbuch, Amir, Neittaanmaki, Pekka, Zheludev, Valery |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 26 pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:1907.01479, arXiv:2001.04899 |
| Databáze: | arXiv |
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