论文标题
Wigner分布和相关的不确定性原理在Octonion线性规范变换的框架中
Wigner Distribution and associated uncertainty principles in the framework of octonion Linear Canonical Transform
论文作者
论文摘要
Octonion傅立叶变换（OFT）的最新概括是八元线性典型变换（OLCT），由于其在颜色图像和信号处理中的应用，在当今时代变得流行。另一方面，Wigner分布（WD）在信号和图像分析中的应用不能排除。在本文中，我们引入了新颖的整体变换，作为八度线性典型变换域（WDOL）中的Wigner分布。我们首先提出了一维WDOL（1DWDOL）的定义，我们扩展了其与1Dolct和1doft的关系。然后探索1DWDOL的几种重要属性，例如重建公式，瑞利定理。其次，我们介绍了三维WDOL（3DWDOL）的定义，并在LCT域（3DWDLCT）中建立了与与Quaternion LCT（WDQLCT）和3DWD相关的WD的关系。然后，我们研究诸如重建公式，雷利定理和与3DWDOL相关的Riemann Lebesgue引理等属性。本文的症结在于制定众所周知的不确定性原则（UPS），包括Heisenbergs Up，对数UP和Hausdorff年轻的不平等现象
The most recent generalization of octonion Fourier transform (OFT) is the octonion linear canonical transform (OLCT) that has become popular in present era due to its applications in color image and signal processing. On the other hand the applications of Wigner distribution (WD) in signal and image analysis cannot be excluded. In this paper, we introduce novel integral transform coined as the Wigner distribution in the octonion linear canonical transform domain (WDOL). We first propose the definition of the one dimensional WDOL (1DWDOL), we extend its relationship with 1DOLCT and 1DOFT. Then explore several important properties of 1DWDOL, such as reconstruction formula, Rayleighs theorem. Second, we introduce the definition of three dimensional WDOL (3DWDOL) and establish its relationships with the WD associated with quaternion LCT (WDQLCT) and 3DWD in LCT domain (3DWDLCT). Then we study properties like reconstruction formula, Rayleighs theorem and Riemann Lebesgue Lemma associated with 3DWDOL. The crux of this paper lies in developing well known uncertainty principles (UPs) including Heisenbergs UP, Logarithmic UP and Hausdorff Young inequality associated with WDOL
