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We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere.
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Driscoll, J. R. and Healy, D. M. J., “Computing Fourier transforms and convolutions on the sphere,” Advances in Applied Mathematics
1994
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Risbo, T., “Fourier transform summation of Legendre series and D D -functions,” J. Geodesy
1996
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Antoine, J.-P. and Vandergheynst, P., “Wavelets on the n-sphere and related manifolds,” J. Math. Phys
1998
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Antoine, J.-P. and Vandergheynst, P., “Wavelets on the 2-sphere: a group theoretical approach,” Applied Comput. Harm. Anal
1999
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Wandelt, B. D. and Górski, K. M., “Fast convolution on the sphere,” Phys. Rev. D
2001
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Healy, D. M. J., Rockmore, D., Kostelec, P. J., and Moore, S. S. B., “FFTs for the 2-sphere – improvements and variations,” J. Fourier Anal. and Appl
2003
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Wiaux, Y., Jacques, L., and Vandergheynst, P., “Correspondence principle between spherical and Euclidean wavelets,” Astrophys. J
2005
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Górski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., and Bartelmann, M., “Healpix – a framework for high resolution discretization and fast analysis of data distributed on the sphere,” Astrophys. J
2005
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McEwen, J. D., Hobson, M. P., and Lasenby, A. N., “A directional continuous wavelet transform on the sphere,” ArXiv
2006
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Narcowich, F. J., Petrushev, P., and Ward, J. D., “Localized tight frames on spheres,” SIAM J. Math. Anal
2006
Cited alongside, same era.
Starck, J.-L., Moudden, Y., Abrial, P., and Nguyen, M., “Wavelets, ridgelets and curvelets on the sphere,” Astron. & Astrophys
2006
Cited alongside, same era.
Wiaux, Y., Jacques, L., Vielva, P., and Vandergheynst, P., “Fast directional correlation on the sphere with steerable filters,” Astrophys. J
2006
Cited alongside, same era.
Vielva, P., Wiaux, Y., Martínez-González, E., and Vandergheynst, P., “Steerable wavelet analysis of CMB structures alignment,” New Astronomy Review
2006
Cited alongside, same era.
McEwen, J. D., Hobson, M. P., Mortlock, D. J., and Lasenby, A. N., “Fast directional continuous spherical wavelet transform algorithms,” IEEE Trans. Sig. Proc
2007
Cited alongside, same era.
Baldi, P., Kerkyacharian, G., Marinucci, D., and Picard, D., “Asymptotics for spherical needlets,” Annals of Statistics
2009
Later among the works it cites.
Hammond, D. K., Wiaux, Y., and Vandergheynst, P., “Wavelet domain Bayesian denoising of string signal in the cosmic microwave background,” Mon. Not. Roy. Astron. Soc
2009
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Wiaux, Y., Jacques, L., and Vandergheynst, P., [ Wavelets on the sphere
2010
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Simons, F. J., Loris, I., Nolet, G., Daubechies, I. C., Voronin, S., Judd, J. S., Vetter, P. A., Charléty, J., and Vonesch, C., “Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity,” Geophysical Journal International
2011
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McEwen, J. D. and Wiaux, Y., “A novel sampling theorem on the sphere,” IEEE Trans. Sig. Proc
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Wiaux, Y., McEwen, J. D., and Vielva, P., “Complex data processing: fast wavelet analysis on the sphere,” J. Fourier Anal. and Appl
2007
Cited alongside, same era.
Marinucci, D., Pietrobon, D., Balbi, A., Baldi, P., Cabella, P., Kerkyacharian, G., Natoli, P., Picard, D., and Vittorio, N., “Spherical needlets for cosmic microwave background data analysis,” Mon. Not. Roy. Astron. Soc
2008
Cited alongside, same era.
Yeo, B., Ou, W., and Golland, P., “On the construction of invertible filter banks on the 2-sphere,” IEEE Trans. Sig. Proc
2008
Cited alongside, same era.
Wiaux, Y., McEwen, J. D., Vandergheynst, P., and Blanc, O., “Exact reconstruction with directional wavelets on the sphere,” Mon. Not. Roy. Astron. Soc
2008
Cited alongside, same era.
McEwen, J. D., Wiaux, Y., Hobson, M. P., Vandergheynst, P., and Lasenby, A. N., “Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures,” Mon. Not. Roy. Astron. Soc
2008
Cited alongside, same era.
2011
Later among the works it cites.
McEwen, J. D., Puy, G., Thiran, J.-P., Vandergheynst, P., Ville, D. V. D., and Wiaux, Y., “Sampling theorems and compressive sensing on the sphere,” in [ Wavelets and Sparsity XIV, SPIE international symposium on optics and photonics
2011
Later among the works it cites.
Leistedt, B., McEwen, J. D., Vandergheynst, P., and Wiaux, Y., “S2LET: A code to perform fast wavelet analysis on the sphere,” Astron. & Astrophys
2012
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Planck Collaboration XXIII, “ Planck
2013
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Planck Collaboration XXV, “ Planck
2013
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Planck Collaboration I, “ Planck
2013
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