{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T20:15:56Z","timestamp":1770668156789,"version":"3.49.0"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100011002","name":"National Natural Science Foundation of China-Yunnan Joint Fund","doi-asserted-by":"publisher","award":["61806027"],"award-info":[{"award-number":["61806027"]}],"id":[{"id":"10.13039\/501100011002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Development Fund","award":["FDCT\/085\/2018\/A2"],"award-info":[{"award-number":["FDCT\/085\/2018\/A2"]}]},{"DOI":"10.13039\/501100004733","name":"Universidade de Macau","doi-asserted-by":"publisher","award":["MYRG2019-00039-FST"],"award-info":[{"award-number":["MYRG2019-00039-FST"]}],"id":[{"id":"10.13039\/501100004733","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Program of Guangzhou","award":["201804010171"],"award-info":[{"award-number":["201804010171"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p> 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 [Formula: see text], [Formula: see text] and its Quaternion Fourier transform is no less than [Formula: see text] 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. <\/jats:p>","DOI":"10.1142\/s0219691321500193","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T16:46:20Z","timestamp":1617727580000},"source":"Crossref","is-referenced-by-count":1,"title":["Discrete uncertainty principle in quaternion setting and application in signal reconstruction"],"prefix":"10.1142","volume":"19","author":[{"given":"Yan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, P. R. 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