Multichannel Poisson denoising and deconvolution on the sphere: application to the Fermi Gamma-ray Space Telescope

J. Schmitt¹, J. L. Starck¹, J. M. Casandjian¹, J. Fadili² and I. Grenier¹

¹ CEA, Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, CEA, IRFU, Service d’Astrophysique, Centre de Saclay, 91191 Gif-Sur-Yvette Cedex, France
e-mail: jeremy.schmitt@cea.fr
² GREYC CNRS-ENSICAEN-Université de Caen, 6 Bd du Maréchal Juin, 14050 Caen Cedex, France

Received: 10 October 2011
Accepted: 10 February 2012

Abstract

A multiscale representation-based denoising method for spherical data contaminated with Poisson noise, the multiscale variance stabilizing transform on the sphere (MS-VSTS), has been previously proposed. This paper first extends this MS-VSTS to spherical two and one dimensions data (2D-1D), where the two first dimensions are longitude and latitude, and the third dimension is a meaningful physical index such as energy or time. We then introduce a novel multichannel deconvolution built upon the 2D-1D MS-VSTS, which allows us to get rid of both the noise and the blur introduced by the point spread function (PSF) in each energy (or time) band. The method is applied to simulated data from the Large Area Telescope (LAT), the main instrument of the Fermi Gamma-ray Space Telescope, which detects high energy gamma-rays in a very wide energy range (from 20 MeV to more than 300 GeV), and whose PSF is strongly energy-dependent (from about 3.5 at 100 MeV to less than 0.1 at 10 GeV).