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On uncertainty principle for the two-sided quaternion linear canonical transform
Journal of Pseudo-Differential Operators and Applications ( IF 0.9 ) Pub Date : 2021-02-06 , DOI: 10.1007/s11868-021-00395-x
Xiaoyu Zhu , Shenzhou Zheng

The quaternion linear canonical transform (QLCT), as a generalized form of the quaternion Fourier transform, is a powerful analyzing tool in image and signal processing. In this paper, we propose five different forms of uncertainty principles for the two-sided QLCT, including logarithmic uncertainty principle, Heisenberg-type uncertainty principle, local uncertainty principle, Benedicks–Amrein–Berthier uncertainty principle and entropic uncertainty principle. These consequences actually describe the quantitative relationships of a quaternion-valued signal in arbitrary two different QLCT domains, and they have great applications in signal recovery and physical quantum.



中文翻译:

双面四元数线性正则变换的不确定性原理

四元数线性典范变换(QLCT)作为四元数傅里叶变换的广义形式,是图像和信号处理中的强大分析工具。在本文中,我们为双面QLCT提出了五种不同形式的不确定性原理,包括对数不确定性原理,Heisenberg型不确定性原理,局部不确定性原理,Benedicks-Amrein-Berthier不确定性原理和熵不确定性原理。这些结果实际上描述了四元数值信号在任意两个不同QLCT域中的定量关系,并且在信号恢复和物理量子中具有很大的应用。

更新日期:2021-02-07
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