球面上的Poisson去噪：在Fermi Gamma Ray Space Telescope中的应用
Poisson Denoising on the Sphere: Application to the Fermi Gamma Ray Space Telescope
摘要：
大面积望远镜（LAT）是费米伽马射线太空望远镜的主要仪器，可探测到能量从20 MeV到300 GeV以上的高能伽马射线。由于缺少光子，两个主要的科学目标，即银河系弥散背景的研究和点源的探测变得复杂。这就是为什么我们需要一个强大的泊松噪声去除方法的球体，这是有效的低计数泊松数据。本文提出了一种新的球上多尺度分解，称为球上多尺度方差稳定变换（MS-VSTS）。该方法基于方差稳定变换（VST），该变换旨在稳定泊松数据集，使得每个稳定样本具有准恒定方差。此外，对于该方法中使用的VST，变换后的数据是渐近高斯的。MS-VSTS包括将数据分解成稀疏的多尺度字典，如小波或曲波，然后对系数应用VST，以获得几乎高斯稳定的系数。在这项工作中，我们使用各向同性未抽取小波变换（IUWT）和曲波变换作为球面多尺度变换。然后，进行二值假设检验，以检测重要系数，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，我们必须提取银河弥漫背景：然后提出了一种扩展的背景分离方法。相反，为了研究银河系的漫射背景，我们用二元掩模去除点源。间隙必须插值：然后提出了一种扩展的修复。该方法，应用于模拟费米LAT数据，证明是自适应的，快速和易于实现。
英文摘要：
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.
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