Uncertainty principle for the quaternion Fourier transform

By Pan Lian. Journal of Mathematical Analysis and Applications, 2018

47 citations recorded by the source corpus.

Abstract The two-sided quaternion Fourier transform was introduced for the analysis of 2D linear time-invariant partial-differential systems. It has been shown to be a powerful tool in image processing. In this paper, several uncertainty inequalities for the two-sided quaternion Fourier transform are given with optimal constants, including the Pitt's inequality, logarithmic uncertainty inequality, Hausdorff–Young inequality, Hirschman's entropy inequality, generalized Heisenberg inequality, local uncertainty principle and qualitative uncertainty principle.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/7e1ce0d546df4ef805493969bda6df6ae6431eed