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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, Swiss Confederation, August 25-29, 2008.



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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