多域光子观测的去噪、去卷积和分解--D4PO算法
Denoising, deconvolving and decomposing multi-domain photon observations- The D4PO algorithm
摘要：
基于光子计数数据的天文成像是一项重要的任务。在这种情况下，我们将展示如何去噪，去卷积，并分解多域光子观测。的主要目标是将准确和动机良好的可能性和先验模型，以提供可靠的估计形态不同，但叠加的光子通量分量存在于数据集中。因此，我们去噪和去卷积光子计数，同时将它们分解成漫射，点状和无趣的背景辐射通量。分解是基于概率层次贝叶斯参数模型的信息场论（IFT）的框架内。与其前身D $^3$ PO相比，D $^4$ PO重建多结构域组分。因此，每个分量被定义在多个独立域（例如，位置和能量）的其自身的直积上。D $^4$ PO具有在分量的每个子域上分别重构相关结构的能力。由此推断的相关性隐含地定义了形态上不同的源分量，除了点状通量的空间相关性。点状源通量在空间上是不相关的。该算法的能力证明了通过一个合成的，但现实的，模拟数据集，提供光谱和空间信息的每个检测到的光子。D $^4$ PO成功地将光子计数图像去噪、去卷积并分解为漫射、点状和背景通量，每个通量都是位置和能量的函数。此外，重建的领域，以及它们的相关结构的不确定性估计提供采用后验密度函数和占域驻留的流形上。
英文摘要：
Astronomical imaging based on photon count data is a non-trivial task. In this context we show how to denoise, deconvolve, and decompose multi-domain photon observations. The primary objective is to incorporate accurate and well motivated likelihood and prior models in order to give reliable estimates about morphologically different but superimposed photon flux components present in the data set. Thereby we denoise and deconvolve photon counts, while simultaneously decomposing them into diffuse, point-like and uninteresting background radiation fluxes. The decomposition is based on a probabilistic hierarchical Bayesian parameter model within the framework of information field theory (IFT). In contrast to its predecessor D$^3$PO, D$^4$PO reconstructs multi-domain components. Thereby each component is defined over its own direct product of multiple independent domains, for example location and energy. D$^4$PO has the capability to reconstruct correlation structures over each of the sub-domains of a component separately. Thereby the inferred correlations implicitly define the morphologically different source components, except for the spatial correlations of the point-like flux. Point-like source fluxes are spatially uncorrelated by definition. The capabilities of the algorithm are demonstrated by means of a synthetic, but realistic, mock data set, providing spectral and spatial information about each detected photon. D$^4$PO successfully denoised, deconvolved, and decomposed a photon count image into diffuse, point-like and background flux, each being functions of location as well as energy. Moreover, uncertainty estimates of the reconstructed fields as well as of their correlation structure are provided employing their posterior density function and accounting for the manifolds the domains reside on.
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