The monogenic Riesz-Laplace wavelet transform
Michael A. Unser, Katarina Balac, Dimitri Van De Ville · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2008
We introduce a family of real and complex wavelet bases of L2(R2) that are directly linked to the Laplace and Riesz op-erators. 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 decomposi-tion. We conclude the paper by presenting a concrete analy-sis example. 1.