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SUMMARY:Functional methods for the design of shiftable and steerable wavel
 et transforms - Michael Unser\, Biomedical Imaging Group\, EPFL\, Lausanne
 \, Switzerland
DTSTART:20100712T103000Z
DTEND:20100712T120000Z
UID:TALK25453@talks.cam.ac.uk
CONTACT:Rachel Fogg
DESCRIPTION:We present two operator-based methods for the construction of 
 wavelets with improved shift-invariance and/or rotation-invariance propert
 ies.\nThe first is inspired by Kingsbury’s dual-tree complex wavelet tra
 nsform and relies on the shifting action of the group of fractional Hilber
 t transform operators. It leads to a precise characterization of the shift
 ability property of complex wavelets whose real and imaginary parts are fu
 nctionally related through the Hilbert transform. \nThe second method is d
 evoted to the construction of steerable wavelets. It relies on an Nth-orde
 r extension of the Riesz transform that has the remarkable property of map
 ping any primary wavelet frame (or basis) of L_2(R^d) into another "steera
 ble" wavelet frame\, while preserving the frame bounds. Concretely\, this 
 means we can design reversible multi-scale decompositions in which the ana
 lysis wavelets (feature detectors) can be spatially rotated in any directi
 on via a suitable linear combination of wavelet coefficients. The concept 
 provides a rigorous functional counterpart to Simoncelli's steerable pyram
 id whose construction was entirely based on digital filter design. It allo
 ws for the specification of wavelets with any order of steerability in any
  number of dimensions. We illustrate the approach with the design of new s
 teerable polyharmonic-spline wavelets that replicate the behavior of the N
 th-order partial derivatives of an isotropic Gaussian kernel and demonstra
 te thei\nr suitability for image processing.\n
LOCATION:LR5\, Engineering\, Department of
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