Two-dimensional quaternion wavelet transform

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• 作者：Mawardi Bahri^a ; ^{mawardibahri@gmail.com"" rel=""nofollow} ; Ryuichi Ashino^b ; ^{ashino@cc.osaka-kyoiku.ac.jp"" rel=""nofollow} ; Ré ; mi Vaillancourt^c ; ^{remi@uottawa.ca"" rel=""nofollow}
• 关键词：Quaternion Fourier transform ; Admissible quaternion wavelets
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：1 September 2011
• 年：2011
• 卷：218
• 期：1
• 页码：10-21
• 全文大小：587 K

文摘

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets.