  The Large Area Telescope (LAT), the main instrument of the Fermi Gamma-Ray
Space Telescope, detects high energy gamma rays with energies from 20 MeV to
more than 300 GeV. The two main scientific ob jectives, the study of the Milky
Way diffuse background and the detection of point sources, are complicated by
the lack of photons. That is why we need a powerful Poisson noise removal
method on the sphere which is efficient on low count Poisson data. This paper
presents a new multiscale decomposition on the sphere for data with Poisson
noise, called Multi-Scale Variance Stabilizing Transform on the Sphere
(MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a
transform which aims to stabilize a Poisson data set such that each stabilized
sample has a quasi constant variance. In addition, for the VST used in the
method, the transformed data are asymptotically Gaussian. MS-VSTS consists of
decomposing the data into a sparse multi-scale dictionary like wavelets or
curvelets, and then applying a VST on the coefficients in order to get almost
Gaussian stabilized coefficients. In this work, we use the Isotropic
Undecimated Wavelet Transform (IUWT) and the Curvelet Transform as spherical
multi-scale transforms. Then, binary hypothesis testing is carried out to
detect significant coefficients, and the denoised image is reconstructed with
an iterative algorithm based on Hybrid Steepest Descent (HSD). To detect point
sources, we have to extract the Galactic diffuse background: an extension of
the method to background separation is then proposed. In contrary, to study the
Milky Way diffuse background, we remove point sources with a binary mask. The
gaps have to be interpolated: an extension to inpainting is then proposed. The
method, applied on simulated Fermi LAT data, proves to be adaptive, fast and
easy to implement.
