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The Monogenic Wavelet Transform

Olhede, SC; Metikas, G; (2009) The Monogenic Wavelet Transform. IEEE T SIGNAL PROCES , 57 (9) 3426 - 3441. 10.1109/TSP.2009.2023397.

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This paper extends the 1-D analytic wavelet transform to the 2-D monogenic wavelet transform. The transformation requires care in its specification to ensure suitable transform coefficients are calculated, and it is constructed so that the wavelet transform may be considered as both local and monogenic. This is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform. Classes of monogenic wavelets are proposed with suitable local properties. It is shown that the monogenic wavelet annihilates anti-monogenic signals, that the monogenic wavelet transform is phase-shift covariant and that the transform magnitude is phase-shift invariant. A simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived. The monogenic wavelet ridges of local plane waves are given.

Type: Article
Title: The Monogenic Wavelet Transform
DOI: 10.1109/TSP.2009.2023397
Keywords: Analytic signal, analytic wavelet transform, Hilbert transform, monogenic signal, Riesz transform, MULTIPLE MORSE WAVELETS, ANALYTIC SIGNAL, IMAGE-ANALYSIS, COEFFICIENTS, SPACE
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/111974
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