The monogenic signal
Felsberg, M.
Sommer, G.
Cognitive Syst. Group, Christian Albrechts Univ., Kiel;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Dec 2001
Volume: 49,
Issue: 12
On page(s): 3136-3144
ISSN: 1053-587X
References Cited: 32
CODEN: ITPRED
INSPEC Accession Number: 7126646
Digital Object Identifier: 10.1109/78.969520
Current Version Published: 2002-08-07
Abstract
This paper introduces a two-dimensional (2-D) 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 2-D signal with the Riesz transformed one yields a
sophisticated 2-D 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 that preserves the split of identity, i.e., the
invariance-equivariance property of signal decomposition, is presented.
This is one of the central properties of the one-dimensional (1-D)
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 with the behavior
of other approaches for a 2-D analytic signal. As a central topic of
this paper, a geometric phase interpretation that is based on the
relation between the 1-D analytic signal and the 2-D monogenic signal
established by the Radon (1986) transform is introduced. Possible
applications of this relationship are sketched, and references to other
applications of the monogenic signal are given
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