Generalized Cramér–Rao inequality and uncertainty relation for fisher information on FrFT

Uncertainty principle plays an important role in signal processing, physics and mathematics and so on. In this paper, four novel uncertainty inequalities including the new generalized Cramér–Rao inequalities and the new uncertainty relations on Fisher information associated with fractional Fourier t...

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Veröffentlicht in:Signal, image and video processing image and video processing, 2020-04, Vol.14 (3), p.499-507
Hauptverfasser: Xu, Guanlei, Xu, Xiaogang, Wang, Xun, Wang, Xiaotong
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Wang, Xiaotong
description Uncertainty principle plays an important role in signal processing, physics and mathematics and so on. In this paper, four novel uncertainty inequalities including the new generalized Cramér–Rao inequalities and the new uncertainty relations on Fisher information associated with fractional Fourier transform (FrFT) are deduced for the first time. These novel uncertainty inequalities extend the traditional Cramér–Rao inequality and the uncertainty relation on Fisher information to the generalized cases. Compared with the traditional Cramér–Rao inequality, the generalized Cramér–Rao inequalities’ bounds are sharper and tighter. In addition, the generalized Cramér–Rao inequalities build the relation between the Cramér–Rao bounds and the FrFT transform angles, which seem to be quaint compared with the traditional counterparts. Furthermore, the generalized Cramér–Rao inequalities give the relation between the FrFT’s variance and FrFT’s gradient’s integral in only one single transform domain, which is fully novel. On the other hand, compared with the traditional uncertainty relation on Fisher information, the newly deduced uncertainty relations on Fisher information yield the sharper and tighter bounds. These deduced inequalities are novel, and they will yield the potential advantage in the parameter estimation in the FrFT domain. Finally, examples are given to show the efficiency of these newly deduced inequalities.
doi_str_mv 10.1007/s11760-019-01571-9
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subjects Computer Imaging
Computer Science
Domains
Fisher information
Fourier transforms
Image Processing and Computer Vision
Inequalities
Inequality
Multimedia Information Systems
Original Paper
Parameter estimation
Pattern Recognition and Graphics
Signal processing
Signal,Image and Speech Processing
Uncertainty principles
Vision
title Generalized Cramér–Rao inequality and uncertainty relation for fisher information on FrFT
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