Wavelets, ridgelets and curvelets on the sphere

2005/09/29 by Jean‐Luc Starck, J.-L. Starck, Jean-Luc Starck +6 · 172 citations
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Artificial intelligence #Computer science #Computer vision #Constant Q transform #Continuous wavelet transform #Curvelet #Discrete wavelet transform #Harmonic wavelet transform #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Pattern recognition (psychology) #Physics #Representation (politics) #Second-generation wavelet transform #Seismic Imaging and Inversion Techniques #Stationary wavelet transform #Wavelet #Wavelet transform #astro-ph

paper · pdf · doi:10.1051/0004-6361:20053246

published in Astronomy and Astrophysics 446(3), 1191-1204 (EDP Sciences) · Accepted for publication in A&A. Manuscript with all figures can be downloaded at http://jstarck.free.fr/aa_sphere05.pdf

arxiv created 2005/09/29 · openalex publication_date 2006/01/20 · arxiv updated 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Astronomical image representation by the curvelet transform

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