期刊
JOURNAL OF MATHEMATICAL IMAGING AND VISION
卷 48, 期 3, 页码 606-624出版社
SPRINGER
DOI: 10.1007/s10851-013-0430-y
关键词
Hypercomplex analysis; Generalized Fourier transform; Clifford-Fourier transform; Geometric Fourier transform; Quaternionic Fourier transform; Convolution product; Color image processing
Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. The present paper develops and studies two conceptually new ways to define convolution products for such transforms. As a by-product, convolution theorems are obtained that will enable the development and fast implementation of new filters for quaternionic signals and systems, as well as for their higher dimensional counterparts.
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