HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere. HEALPix—the Hierarchical Equal Area isoLatitude Pixelization—is a versatile structure for the pixelization of data on the sphere. An associated library of computational algorithms and visualization software supports fast scientific applications executable directly on discretized spherical maps generated from very large volumes of astronomical data. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background experiments (e.g., BOOMERANG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including, e.g., Planck, Herschel, SAFIR, and the Beyond Einstein inflation probe. In this paper we consider the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere. We demonstrate how these are explicitly satisfied by HEALPix.

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  1. Cheng, Dan; Cammarota, Valentina; Fantaye, Yabebal; Marinucci, Domenico; Schwartzman, Armin: Multiple testing of local maxima for detection of peaks on the (celestial) sphere (2020)
  2. Drake, Kathryn P.; Wright, Grady B.: A fast and accurate algorithm for spherical harmonic analysis on HEALPix grids with applications to the cosmic microwave background radiation (2020)
  3. Le Gia, Quoc Thong; Sloan, Ian H.; Womersley, Robert S.; Wang, Yu Guang: Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere (2020)
  4. Stough, T.; Cressie, N.; Kang, E. L.; Michalak, A. M.; Sahr, K.: Spatial analysis and visualization of global data on multi-resolution hexagonal grids (2020)
  5. Wang, Yu Guang; Zhuang, Xiaosheng: Tight framelets and fast framelet filter bank transforms on manifolds (2020)
  6. Broadbridge, Phil; Kolesnik, Alexander D.; Leonenko, Nikolai; Olenko, Andriy: Random spherical hyperbolic diffusion (2019)
  7. Constantin Steppa, Tim L. Holch: HexagDLy - Processing hexagonally sampled data with CNNs in PyTorch (2019) not zbMATH
  8. Daniel Fryer, Andriy Olenko: Spherical data handling and analysis with R package rcosmo (2019) arXiv
  9. Fryer, Daniel; Olenko, Andriy: Spherical data handling and analysis with R package rcosmo (2019)
  10. Tahir, Noraiz; De Paolis, Francesco; Qadir, Asghar; Nucita, Achille A.: Seeing the halo rotation of nearby spiral galaxies using Planck data (2019)
  11. Chen, Xiaojun; Womersley, Robert S.: Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere (2018)
  12. Creasey, Peter E.; Lang, Annika: Fast generation of isotropic Gaussian random fields on the sphere (2018)
  13. Fan, Minjie; Paul, Debashis; Lee, Thomas C. M.; Matsuo, Tomoko: A multi-resolution model for non-Gaussian random fields on a sphere with application to ionospheric electrostatic potentials (2018)
  14. Fan, Minjie; Paul, Debashis; Lee, Thomas C. M.; Matsuo, Tomoko: Modeling tangential vector fields on a sphere (2018)
  15. Leonenko, Nikolai N.; Taqqu, Murad S.; Terdik, Gyorgy H.: Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem (2018)
  16. McEwen, Jason D.; Durastanti, Claudio; Wiaux, Yves: Localisation of directional scale-discretised wavelets on the sphere (2018)
  17. Womersley, Robert S.: Efficient spherical designs with good geometric properties (2018)
  18. Durastanti, Claudio: Tail behavior of Mexican needlets (2017)
  19. Holhoş, Adrian; Roşca, Daniela: Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere (2017)
  20. Michaels, T.: Equidistributed icosahedral configurations on the sphere (2017)

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