Wavelets, ridgelets and curvelets on the sphere

Details Wavelets, ridgelets and curvelets on the sphere Wavelets, ridgelets and curvelets on the sphere

2005-09-29

arxiv.org/abs/astro-ph/0509883v1

Astronomy and Astrophysics

Astrophysics

Accepted for publication in A&A. Manuscript with all figures can be downloaded at http://jstarck.free.fr/aa_sphere05.pdf

Scientific paper

10.1051/0004-6361:20053246

We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be inverted i.e. we can exactly reconstruct the original data from its coefficients in either representation. Several applications are described. We show how these transforms can be used in denoising and especially in a Combined Filtering Method, which uses both the wavelet and the curvelet transforms, thus benefiting from the advantages of both transforms. An application to component separation from multichannel data mapped to the sphere is also described in which we take advantage of moving to a wavelet representation.

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