Tokyo lecture of Anna Kit Ian Kou: The Applications of Quaternion Linear Canonical Transforms


Speaker: Prof. Anna Kit Ian Kou, Department of Mathematics, University of Macao, Macao
Title: The Applications of Quaternion Linear Canonical Transforms
Date: Monday, 19th December
Time: 12:45-13:45
Place: International Christian University, Science Hall, First Floor, North Wing, Room: N101 (back)
Building No. 4 on the following map: http://www.icu.ac.jp/en/about/campus/
Campus access instructions: http://www.icu.ac.jp/en/about/access/index.html

Host: Eckhard Hitzer (hitzer_AT_icu.ac.jp), College of Liberal Arts, ICU

Abstract: The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. As an application, examples of envelope detection demonstrate the effectiveness of our approach.

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