Residential College | false |
Status | 已發表Published |
Discrete uncertainty principle in quaternion setting and application in signal reconstruction | |
Yan Yang1; Kit Ian Kou2; Cuiming Zou3 | |
2021-05 | |
Source Publication | International Journal of Wavelets, Multiresolution and Information Processing |
ISSN | 0219-6913 |
Volume | 19Issue: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. |
Keyword | Discrete Uncertainty Principle Quaternion Fourier Transform Signal Reconstruction |
DOI | 10.1142/S0219691321500193 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Computer Science ; Mathematics |
WOS Subject | Computer Science, Software Engineering ; Mathematics, Interdisciplinary Applications |
WOS ID | WOS:000707381400001 |
Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE |
Scopus ID | 2-s2.0-85106193344 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | University of Macau |
Corresponding Author | Kit Ian Kou |
Affiliation | 1.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 Affilication | Faculty of Science and Technology |
Recommended Citation GB/T 7714 | Yan Yang,Kit Ian Kou,Cuiming Zou. Discrete uncertainty principle in quaternion setting and application in signal reconstruction[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2021, 19(5). |
APA | Yan Yang., Kit Ian Kou., & Cuiming Zou (2021). Discrete uncertainty principle in quaternion setting and application in signal reconstruction. International Journal of Wavelets, Multiresolution and Information Processing, 19(5). |
MLA | Yan Yang,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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