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Radial 3D-Needlets on the Unit Ball

  • Claudio Durastanti (a1), Yabebal T. Fantaye (a2), Frode K. Hansen (a3), Domenico Marinucci (a4) and Isaac Z. Pesenson (a5)...

Abstract

We present a simple construction of spherical wavelets for the unit ball, which we label Radial 3D Needlets. We envisage an experimental framework where data are collected on concentric spheres with the same pixelization at different radial distances from the origin. The unit ball is hence viewed as a tensor product of the unit interval with the unit sphere: a set of eigenfunctions is therefore defined on the corresponding Laplacian operator. Wavelets are then constructed by a smooth convolution of the projectors defined by these eigenfunctions. Localization properties may be rigorously shown to hold in the real and harmonic domain, and an exact reconstruction formula holds; the system allows a very convenient computational implementation.

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References

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Bobin, J., Sureau, F., Paykari, P., Rassat, A., Basak, S., & Starck, J.-L. 2013, A&A, 553, L4
Donzelli, S., Hansen, F. K., Liguori, M., Marinucci, D., & Matarrese, S. 2012, ApJ, 755, 19
Faÿ, G., Guilloux, F., Betoule, M., Cardoso, J.-F., Delabrouille, J., & Le Jeune, M. 2008, Phys. Rev. D, D78:083013
Geller, D. & Mayeli, A. 2009, Math. Z. 1, 263
Gorski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., & Bartelman, M. 2005, ApJ, 622
Lanusse, F., Rassat, A., & Starck, J. L. 2012, A&A 540, A9
Laureijs, R., Duvet, L., Escudero Sanz, I., Gondoin, P., Lumb, D. H., Oosterbroek, T., & Saavedr ACriado, G. 2010, The Euclid Mission SPIE Proceedings 7731
Leistedt, B. & McEwen, J. D. 2012, IEEE Trans. on Sign. Proc. 60, 12
Marinucci, D., Pietrobon, D., Balbi, A., Baldi, P., Cabella, P., Kerkyacharian, G., Natoli, P., Picard, D. & Vittorio, N. 2008, MNRAS, 383, 2
McEwen, J. D., Vielva, P., Wiaux, Y., Barreiro, R. B., Cayón, I., Hobson, M. P., Lasenby, A. N., Martí nez-González, E., & Sanz, J. L. 2007, J. Fourier Anal. Appl., 13, 4
Narcowich, F. J., Petrushev, P., & Ward, J. D. 2006, SIAM Journal of Mathematical Analysis, 38
Narcowich, F. J., Petrushev, P., & Ward, J. D. 2006, Journal of Functional Analysis, 238, 2
Pesenson, I. Z. 2014, submitted
Pietrobon, D., Amblard, A., Balbi, A., Cabella, P., Cooray, A., & Marinucci, D. 2008, Phys. Rev. D, D78:103504
Planck Collaboration, 2013, to appear on A&A
Starck, J.-L., Moudden, Y., Abrial, P., & Nguyen, M. 2006, A&A, 446
Starck, J.-L., Murtagh, F., & Fadili, J.Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity (Cambridge University Press)
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Keywords

Radial 3D-Needlets on the Unit Ball

  • Claudio Durastanti (a1), Yabebal T. Fantaye (a2), Frode K. Hansen (a3), Domenico Marinucci (a4) and Isaac Z. Pesenson (a5)...

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