000115077 001__ 115077
000115077 005__ 20190316234111.0
000115077 0247_ $$2doi$$a10.1111/j.1365-2966.2008.13448.x
000115077 02470 $$2DAR$$a12870
000115077 02470 $$2ISI$$a000257781400024
000115077 037__ $$aARTICLE
000115077 245__ $$aExact reconstruction with directional wavelets on the sphere
000115077 269__ $$a2008
000115077 260__ $$c2008
000115077 336__ $$aJournal Articles
000115077 520__ $$aA new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.
000115077 6531_ $$afilter banks
000115077 6531_ $$awavelet on the sphere
000115077 6531_ $$acosmology
000115077 6531_ $$aLTS2
000115077 700__ $$0240427$$g163268$$aWiaux, Y.
000115077 700__ $$0242931$$g201873$$aMcEwen, J. D.
000115077 700__ $$0240428$$g120906$$aVandergheynst, P.
000115077 700__ $$0241714$$g104555$$aBlanc, O.
000115077 773__ $$j388$$tMon. Not. R. Astron. Soc.$$q770
000115077 8564_ $$uhttp://www.blackwellpublishing.com/journal.asp?ref=0035-8711$$zURL
000115077 8564_ $$uhttps://infoscience.epfl.ch/record/115077/files/steerwavesphere-arXiv-0712.3519v3.pdf$$zn/a$$s644644
000115077 909C0 $$xU10380$$0252392$$pLTS2
000115077 909CO $$ooai:infoscience.tind.io:115077$$qGLOBAL_SET$$pSTI$$particle
000115077 937__ $$aEPFL-ARTICLE-115077
000115077 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000115077 980__ $$aARTICLE