论文标题
源自多项式花纹的定向小波包数据包
Directional wavelet packets originating from polynomial splines
论文作者
论文摘要
该论文介绍了准分析复合物值小波包（WPS）的多功能库，该库源自任意阶的多项式花纹。准分析WPS的实际部分是[1]中设计的基于常规的基于样条的正顺序WPS。假想的部分是从常规WPS的Hilbert变换中得出的所谓互补正顺序WP，与对称的常规WPS不同，是反对称的。 1D准分析WPS的张量产品可在多个方向上提供2D WPS的多样性。例如，一组第四级WPS包含62个不同的方向。所呈现的WPS的性质是精制的频率分辨率，无限数量的波形的方向性，波形的（反）对称性以及具有多种频率的波形的窗口振荡结构。定向WP具有强大的潜力，可以在各种图像处理应用中使用，例如恢复降解的图像以及从图像中提取特征特征。
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.
