Steerable wavelet frames based on the Riesz transform

Authors:
Stefan Held;Martin Storath;Peter Massopust;Brigitte Forster
Affiliations:
Zentrum Mathematik, Technische Universität München, Germany;Zentrum Mathematik, Technische Universität München, Germany;Institute of Biomathematics and Biometry, Helmholtz Zentrum München, Germany;Zentrum Mathematik, Technische Universität München, Germany and Institute of Biomathematics and Biometry, Helmholtz Zentrum München, Germany
Venue:
IEEE Transactions on Image Processing
Year:
2010

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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.