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.

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。