Uncertainty principle in random quaternion domains

In this paper, we establish Donoho and Stark's uncertainty principle in the framework of quaternionic analysis for random signals, where a probability measure is involved in our generalizations. In particular, the results are given for the right-sided and the two-sided quaternion Fourier transf...

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Bibliographic Details
Published in:Digital signal processing 2023-05, Vol.136, p.103988, Article 103988
Main Authors: Dang, Pei, Mai, Weixiong, Pan, Wenliang
Format: Article
Language:English
Subjects:
Donoho and Stark's uncertainty principle
Quaternion Fourier transform
Random quaternion-valued signal
Signal recovery
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Summary:In this paper, we establish Donoho and Stark's uncertainty principle in the framework of quaternionic analysis for random signals, where a probability measure is involved in our generalizations. In particular, the results are given for the right-sided and the two-sided quaternion Fourier transform, respectively. In the last section we will apply the obtained results in recovery problem for random signals. Several numerical experiments are used to demonstrate the performance of the proposed methods.
ISSN:1051-2004
1095-4333
DOI:10.1016/j.dsp.2023.103988