Publication
Title
Connecting spatial and frequency domains for the quaternion Fourier transform
Author
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.
Language
English
Source (journal)
Applied mathematics and computation. - New York, N.Y.
Publication
New York, N.Y. : 2015
ISSN
0096-3003
Volume/pages
271(2015), p. 581-593
ISI
000364538300052
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 09.12.2015
Last edited 09.06.2017
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