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Steerable Wavelet Frames Based on the Riesz Transform
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DOI：10.1109/TIP.2009.2036713.png)
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Abstract
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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.
Keywords:
Analytical signal
Clifford algebra
contrast enhancement
descreening
Hilbert transform
monogenic signal
phase
phase direction
Riesz transform
steerable filters
wavelet
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