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Discrete uncertainty principle in quaternion setting and application in signal reconstruction
Yang, Yan1; Kou, Kit Ian2; Zou, Cuiming3
2021-09-01
Source PublicationInternational Journal of Wavelets, Multiresolution and Information Processing
ISSN0219-6913
Volume19Issue:5
Abstract

In this paper, a novel discrete uncertainty principle associated with discrete Quaternion Fourier transform is established to give the relationship between the nonzero numbers of the discrete quaternion-valued signals and their Quaternion Fourier transforms. We obtain that the product of the numbers of nonzero elements of a sequence f(t,s), (t = 0, 1,...,M - 1,s = 0, 1,...,N - 1) and its Quaternion Fourier transform is no less than MN and the result is sharp. Then we extend the uncertainty principle of discrete signals proved by Donoho and Starkin to two dimensional case. It suggests how sparsity helps in the recovery of missing frequency. The experimental results on the recovery of Lena also demonstrate the necessity of the two-dimensional discrete uncertainty principle associated with Quaternion Fourier transforms.

KeywordDiscrete Uncertainty Principle Quaternion Fourier Transform Signal Reconstruction
DOI10.1142/S0219691321500193
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000707381400001
Scopus ID2-s2.0-85106193344
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorKou, Kit Ian
Affiliation1.School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai, 519082, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macao
3.College of Science, Huazhong Agricultural University, Wuhan, 430070, China
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Yang, Yan,Kou, Kit Ian,Zou, Cuiming. Discrete uncertainty principle in quaternion setting and application in signal reconstruction[J]. International Journal of Wavelets, Multiresolution and Information Processing,2021,19(5).
APA Yang, Yan,Kou, Kit Ian,&Zou, Cuiming.(2021).Discrete uncertainty principle in quaternion setting and application in signal reconstruction.International Journal of Wavelets, Multiresolution and Information Processing,19(5).
MLA Yang, Yan,et al."Discrete uncertainty principle in quaternion setting and application in signal reconstruction".International Journal of Wavelets, Multiresolution and Information Processing 19.5(2021).
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