EPFL | Biomedical Imaging Group | Monogenic Wavelets

The Monogenic Riesz-Laplace Wavelet Transform

M. Unser, K. Balać, D. Van De Ville

Proceedings of the Sixteenth European Signal Processing Conference (EUSIPCO'08), Lausanne VD, Switzerland, August 25-29, 2008, in press.

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We introduce a family of real and complex wavelet bases of L₂(ℝ²) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a real basis into a complex one. We propose to use such a Riesz pair of wavelet transforms 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 derive a corresponding wavelet-domain method for estimating the underlying instantaneous frequency of the signal. We also provide a simple mechanism for improving the shift and rotation-invariance of the wavelet decomposition. We conclude the paper by presenting a concrete analysis example.

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