Wavelets, ridgelets, curvelets on the sphere, and applications

Y. Moudden; P. Abrial; J.-L. Starck

doi:10.1117/12.619197

17 September 2005 Wavelets, ridgelets, curvelets on the sphere, and applications

Y. Moudden, P. Abrial, J.-L. Starck

Proceedings Volume 5914, Wavelets XI; 59140R (2005) https://doi.org/10.1117/12.619197
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

Analyzing data mapped to the sphere as may occur in a range of applications in geophysics, medical imaging or astrophysics, requires specific tools. This paper describes new multiscale decompositions for spherical images namely the isotropic undecimated wavelet transform, the ridgelet transform and the curvelet transform each of which is invertible. 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 where we take advantage of the spatiospectral localization on the sphere provided by the spherical wavelet functions.

Citation Download Citation

Y. Moudden, P. Abrial, and J.-L. Starck "Wavelets, ridgelets, curvelets on the sphere, and applications", Proc. SPIE 5914, Wavelets XI, 59140R (17 September 2005); https://doi.org/10.1117/12.619197

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