Left invariant evolution equations on Gabor transforms

R. Duits, H. Führ, B.J Janssen

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

By means of the unitary Gabor transform one can relate operators on signals to operators on the space of Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding operator on the reproducing kernel space of Gabor transforms must be left invariant, i.e. it should commute with the left regular action of the reduced Heisenberg group H r . By using the left invariant vector fields on H r and the corresponding left-invariant vector fields on phase space in the generators of our transport and diffusion equations on Gabor transforms we naturally employ the essential group structure on the domain of a Gabor transform. Here we mainly restrict ourselves to non-linear adaptive left-invariant convection (reassignment), while maintaining the original signal.
Original languageEnglish
Title of host publicationMathematical Methods for Signal and Image Analysis and Representation
EditorsL.M.J. Florack, R. Duits, G. Jongbloed, M.N.M. Lieshout, van, P.L. Davies
Place of PublicationLondon
PublisherSpringer
Pages137-158
ISBN (Print)978-1-4471-2352-1
DOIs
Publication statusPublished - 2012

Publication series

NameComputational Imaging and Vision
Volume41
ISSN (Print)1381-6446

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Duits, R., Führ, H., & Janssen, B. J. (2012). Left invariant evolution equations on Gabor transforms. In L. M. J. Florack, R. Duits, G. Jongbloed, M. N. M. Lieshout, van, & P. L. Davies (Eds.), Mathematical Methods for Signal and Image Analysis and Representation (pp. 137-158). (Computational Imaging and Vision; Vol. 41). London: Springer. https://doi.org/10.1007/978-1-4471-2353-8_8