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Multiple multidimensional morse wavelets

Metikas, G; Olhede, SC; (2007) Multiple multidimensional morse wavelets. IEEE T SIGNAL PROCES , 55 (3) 921 - 936. 10.1109/TSP.2006.887562. Green open access

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This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved.

Type: Article
Title: Multiple multidimensional morse wavelets
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2006.887562
Keywords: analytic signal, image analysis, monogenic signal, Riesz transform, scalogram, wavelets, SIGNALS, LOCALIZATION, EXTENSION, SPECTRUM, PHASE
UCL classification: UCL
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: https://discovery.ucl.ac.uk/id/eprint/5423
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