Talks given at NuHAG events

Locally supported orthogonal wavelet bases on the sphere via stereographic projection

  Jean-Pierre Antoine

  given at  strobl07 (21.06.07 16:15)
  id:  618
  length:  25min
  status:  accepted
  type:  talk
The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding $L^2$ spaces. As it is known, this map in turn leads to an equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inverse stereographic projection, to a wavelet on the sphere. In this work, we apply this procedure to orthogonal bases
of locally supported wavelets in the plane and get similar bases on the sphere. Numerical examples are given and compared with the results obtained by other types of spherical wavelet frames.

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