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Scientific article
English

Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform

Contributors

Unser, Michael; Sage, Daniel; Van De Ville, Dimitri

Published in

IEEE transactions on image processing, vol. 18, no. 11, p. 2402-2418

Publication date

2009

Abstract

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L(2) (R(2)) that involves a single Mexican-hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency. We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.

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UNIGE research groups

Citation (ISO format)

UNSER, Michael, SAGE, Daniel, VAN DE VILLE, Dimitri. Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform. In: IEEE transactions on image processing, 2009, vol. 18, n° 11, p. 2402–2418. doi: 10.1109/TIP.2009.2027628

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Additional URL for this publication

http://ieeexplore.ieee.org/ielx5/83/5286712/05164973.pdf?tp=&arnumber=5164973&isnumber=5286712

Journal ISSN

1057-7149
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Technical informations

Creation

23/04/2012 13:32:41

First validation

23/04/2012 13:32:41

Update

14/03/2023 17:28:06

Status update

14/03/2023 17:28:06

Last indexation

29/10/2024 19:39:35
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