# Spherical Continuous Wavelet Transforms arising from sections of the Lorentz group

Milton Ferreira

given at  strobl07 (18.06.07 16:15)
id:  563
length:  25min
status:  accepted
type:  talk
LINK-Presentation:
ABSTRACT:
We consider the conformal group of the unit sphere $S^{n-1},$ the Lorentz group $Spin^+(1,n)$ (double covering group of the proper Lorentz group $SO_0(1,n)$) for the study of spherical continuous wavelet transforms (SCWT). The parameter space is determined by a factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We define admissible local and global sections and we study some families of sections that give rise to SCWT. These SCWT extend the SCWT of J.P. Antoine and P. Vandergheynst , which itself arises from the fundamental section of our homogeneous space.
The advantage of these new SCWT is that they incorporate relativistic movements on the unit sphere which are suitable for signal processing on the unit sphere.

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