标题： 球面上的泊松去噪：应用于费米伽马射线太空望远镜 显示英文标题

标题： Poisson Denoising on the Sphere: Application to the Fermi Gamma Ray Space Telescope

摘要： 大型面积望远镜（LAT），费米伽马射线空间望远镜的主要仪器，能够检测能量从20 MeV到超过300 GeV的高能伽马射线。两个主要的科学目标，即研究银河系弥散背景和检测点源，由于光子的缺乏而变得复杂。这就是为什么我们需要一种在球面上高效的低计数泊松数据去噪方法。本文提出了一种用于具有泊松噪声的数据的球面上的新多尺度分解方法，称为球面多尺度方差稳定变换（MS-VSTS）。该方法基于方差稳定变换（VST），这是一种旨在稳定泊松数据集的变换，使得每个稳定后的样本具有准常方差。此外，用于该方法的VST变换后的数据渐近服从高斯分布。MS-VSTS包括将数据分解为类似小波或曲线波的稀疏多尺度字典，然后对系数应用VST以获得几乎高斯的稳定系数。在这项工作中，我们使用各向同性未抽样小波变换（IUWT）和曲线波变换作为球面上的多尺度变换。然后进行二元假设检验以检测显著系数，并使用基于混合最速下降（HSD）的迭代算法重建去噪图像。为了检测点源，我们必须提取银河系弥散背景：然后提出了该方法的背景分离扩展。相反，为了研究银河系弥散背景，我们使用二值掩码去除点源。必须对间隙进行插值：然后提出了填补扩展。该方法应用于模拟的费米 LAT 数据，证明是自适应的、快速且易于实现的。 显示英文摘要

摘要： 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.