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SUMMARY:Complex-valued wavelets\, the dual tree\, and Hilbert pairs: why t
 hese lead to shift invariance and directional multi-dimensional wavelets -
  Nick Kingsbury (Signal Processing &amp\; Communications Group\, Departmen
 t of Engineering\, University of Cambridge)
DTSTART:20120223T140000Z
DTEND:20120223T143000Z
UID:TALK36136@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:This talk will discuss some of the interesting mathematical pr
 operties of the dual tree wavelet construction\, when it is used to genera
 te analytic complex-valued wavelets.  We shall show how the requirement fo
 r analyticity (zero energy at negative frequencies) implies that the wavel
 et bases from the two parts of the dual tree should form a Hilbert transfo
 rm pair\, and how this leads to the half-sample delay condition between th
 e lowpass (scaling function) filters of each tree.  It will then be shown 
 how this results in approximate shift invariance of the complex wavelet tr
 ansform\, and the elegant Q-shift filter solution to this condition will b
 e given.  We will then discuss how the analytic nature of the wavelets in 
 1-D allows separable wavelet filters in higher dimensional spaces to be hi
 ghly directionally selective. Finally we will present a wide range of appl
 ications for the dual-tree wavelets\, including denoising\, regularisation
 \, motion / displacement estimation of 2-D and 3-D datasets\, and object r
 ecognition.\n\nThe slides of the talk are online at http://www.damtp.cam.a
 c.uk/user/cbs31/MI_Cambridge/MathAndInfo_Network_files/nickkingsburytalk.p
 df
LOCATION:MR2\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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