Title
Connecting spatial and frequency domains for the quaternion Fourier transform Connecting spatial and frequency domains for the quaternion Fourier transform
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Applied mathematics and computation. - New York, N.Y.
Volume/pages
271(2015) , p. 581-593
ISSN
0096-3003
ISI
000364538300052
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined 'Mustard' convolution behaves nicely in the frequency domain, but complicates the corresponding spatial domain analysis. The present paper analyses in detail the correspondence between classical convolution and the new Mustard convolution. In particular, an expression is derived that allows one to write classical convolution as a finite linear combination of suitable Mustard convolutions. This result is expected to play a major role in the further development of quaternion image processing, as it yields a formula for the qFT spectrum of the classical convolution. (C) 2015 Elsevier Inc. All rights reserved.
E-info
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https://repository.uantwerpen.be/docman/iruaauth/f0c43a/129541.pdf
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