Steerable wavelet frames based on the Riesz transform

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Stefan HeldBrigitte Forster

Abstract

We consider an extension of the 1-D concept of analytical wavelet to n-D which is by construction compatible with rotations. This extension, called a monogenic wavelet, yields a decomposition of the wavelet coefficients into amplitude, phase, and phase direction. The monogenic wavelet is based on the hypercomplex monogenic signal which is defined using Riesz transforms and perfectly isotropic wavelets frames. Employing the new concept of Clifford frames, we can show that the monogenic wavelet generates a wavelet frame. Furthermore, this approach yields wavelet frames that are steerable with respect to direction. Applications to descreening and contrast enhancement illustrate the versatility of this approach to image analysis and reconstruction.

References

Aug 8, 2001·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·K G LarkinM A Oldfield
Jul 1, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Wai Lam ChanRichard G Baraniuk
Nov 1, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Dimitri Van De Ville, Michael Unser
Jul 17, 2009·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Michael UnserDimitri Van De Ville

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Citations

Nov 30, 2012·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Raphaël SoulardChristine Fernandez-Maloigne
Dec 25, 2009·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Michael Unser, Dimitri Van De Ville
Jul 4, 2012·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Nicolas Chenouard, Michael Unser
Apr 12, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Michael UnserDimitri Van de Ville
Mar 29, 2016·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Pedram PadMichael Unser
May 14, 2016·PloS One·Duy Hoang ThaiCarsten Gottschlich
Apr 15, 2017·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society· Ganggang Dong Wei Wang
Oct 2, 2020·Medical & Biological Engineering & Computing·Brandon RebholzMohamed Almekkawy
Feb 6, 2018·Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society·Ranveer JoyseereeAdrien Depeursinge

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