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The monogenic signal
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
2001 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, Vol. 49, no 12, 3136-3144 p.Article in journal (Refereed) Published
Abstract [en]

This paper introduces a two-dimensional generalization of the analytic signal. This novel approach is based on the Riesz transform, which is used instead of the Hilbert transform. The combination of a 2D signal with the Riesz transformed one yields a sophisticated 2D analytic signal, the monogenic signal. The approach is derived analytically from irrotational and solenoidal vector fields. Based on local amplitude and local phase, an appropriate local signal representation is presented which preserves the split of identity, i.e., the invariance – equivariance property of signal decomposition. This is one of the central properties of the 1D analytic signal that decomposes a signal into structural and energetic information. We show that further properties of the analytic signal concerning symmetry, energy, allpass transfer function, and orthogonality are also preserved, and we compare this to the behavior of other approaches for a 2D analytic signal. As a central topic of this paper, a geometric phase interpretation is introduced which is based on the relation between the 1D analytic signal and the 2D monogenic signal established by the Radon transform. Possible applications of this relationship are sketched and references to other applications of the monogenic signal are given. This report is a revised version of the technical report 2009 [7], and therefore supercedes it.

Place, publisher, year, edition, pages
2001. Vol. 49, no 12, 3136-3144 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-21588DOI: 10.1109/78.969520OAI: diva2:241550
©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Michael Felsberg and Gerald Sommer, The monogenic signal, 2001, IEEE Transactions on Signal Processing, (49), 12, 3136-3144. Available from: 2009-10-04 Created: 2009-10-04 Last updated: 2010-02-10

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