Communications and Networking. 13th EAI International Conference, ChinaCom 2018, Chengdu, China, October 23-25, 2018, Proceedings

Research Article

The Quaternion-Fourier Transform and Applications

  • @INPROCEEDINGS{10.1007/978-3-030-06161-6_15,
        author={Shanshan Li and Jinsong Leng and Minggang Fei},
        title={The Quaternion-Fourier Transform and Applications},
        proceedings={Communications and Networking. 13th EAI International Conference, ChinaCom 2018, Chengdu, China, October 23-25, 2018, Proceedings},
        proceedings_a={CHINACOM},
        year={2019},
        month={1},
        keywords={Quaternion analysis Paley-Wiener theorem Quaternion-Fourier transform},
        doi={10.1007/978-3-030-06161-6_15}
    }
    
  • Shanshan Li
    Jinsong Leng
    Minggang Fei
    Year: 2019
    The Quaternion-Fourier Transform and Applications
    CHINACOM
    Springer
    DOI: 10.1007/978-3-030-06161-6_15
Shanshan Li1,*, Jinsong Leng1,*, Minggang Fei1,*
  • 1: University of Electronic Science and Technology of China
*Contact email: shanshanli@swun.cn, lengjs@uestc.edu.cn, fei@uestc.edu.cn

Abstract

It is well-known that the Fourier transforms plays a critical role in image processing and the corresponding applications, such as enhancement, restoration and compression. For filtering of gray scale images, the Fourier transform in is an important tool which converts the image from spatial domain to frequency domain, then by applying filtering mask filtering is done. To filter color images, a new approach is implemented recently which uses hypercomplex numbers (called Quaternions) to represent color images and uses Quaternion-Fourier transform for filtering. The quaternion Fourier transform has been widely employed in the colour image processing. The use of quaternions allow the analysis of color images as vector fields, rather than as color separated components. In this paper we mainly focus on the theoretical part of the Quaternion Fourier transform: the real Paley-Wiener theorems for the Quaternion-Fourier transform on for Quaternion-valued Schwartz functions and -functions, which generalizes the recent results of real Paley-Wiener theorems for scalar- and quaternion-valued -functions.