Title :
Statistical properties of spherical wavelets systems
Author :
Marinucci, Domenico ; Vadlamani, Sreekar
Author_Institution :
Dept. of Math., Univ. of Rome Tor Vergata, Rome, Italy
Abstract :
We review some spherical wavelets systems and their statistical properties, with a view to applications in Cosmological/Astrophysical data analysis. In particular, we consider the analysis of Gaussian, isotropic random fields, and we focus on the geometric characterization of wavelet fields emerging in band-limited reconstructions. More precisely, we recall how to provide exact expression for Minkowski functionals evaluated on needlet fields, and how to exploit them to derive sharp bounds on excursion probabilities; the latter provide flexible tools to test for nonGaussianity and anisotropies on CMB data.
Keywords :
Gaussian processes; cosmic background radiation; cosmology; data analysis; geometry; probability; random processes; wavelet transforms; CMB data; Gaussian analysis; Minkowski functional; astrophysical data analysis; band-limited reconstruction; cosmological data analysis; excursion probabilities; geometric characterization; isotropic random fields; needlet fields; nonGaussianity; spherical wavelets system; statistical properties; wavelet field; Data analysis; Estimation; Geometry; Harmonic analysis; Microwave integrated circuits; Standards; Wavelet analysis; Cosmology and Astrophysics; Geometry of Random Fields; Spherical Data; Wavelets;
Conference_Titel :
Image Processing (ICIP), 2014 IEEE International Conference on
Conference_Location :
Paris
DOI :
10.1109/ICIP.2014.7026213
