基于深度学习的快速点扩散函数建模
Fast Point Spread Function Modeling with Deep Learning
摘要：
建立宽视场观测的点扩散函数（PSF）模型对于包括弱引力透镜在内的许多天体物理应用和宇宙学探测都是至关重要的。PSF模糊了任何记录物体的图像，因此在从天文图像推断星系属性时需要考虑在内。在宇宙剪切的情况下，PSF是系统误差的主要来源之一，必须小心处理，以避免宇宙学参数的偏差。最近，已经开发了在蒙特卡罗控制环（$MCCL$）框架内校准剪切测量的正演模拟方法。这些方法通常需要模拟大量的宽视场图像，因此，模拟需要非常快，但在关键特征（如PSF图案）中具有真实的属性。因此，这样的正演建模方法需要非常灵活的PSF模型，该模型能够快速评估并且其参数能够从勘测数据可靠地估计。我们提出了一种基于快速深度学习方法来估计其自由参数的PSF模型，以满足这些要求。我们展示了我们的方法公开可用的SDSS数据。我们通过主成分分析提取SDSS样本的最重要的特征。接下来，我们基于固定基础轮廓的扰动来构建模型，确保它捕获这些特征。然后，我们训练一个卷积神经网络估计的自由参数的模型从噪声图像的点扩展函数。这使我们能够渲染每个恒星的模型图像，我们将其与SDSS恒星进行比较，以评估我们方法的性能。我们发现，我们的方法是能够准确地再现SDSS PSF在像素级，这是由于模型评估和参数估计的速度，提供了良好的前景，将我们的方法纳入$MCCL$框架。
英文摘要：
Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops ($MCCL$) framework have been developed. These methods typically require simulating a large amount of wide-field images, thus, the simulations need to be very fast yet have realistic properties in key features such as the PSF pattern. Hence, such forward modeling approaches require a very flexible PSF model, which is quick to evaluate and whose parameters can be estimated reliably from survey data. We present a PSF model that meets these requirements based on a fast deep-learning method to estimate its free parameters. We demonstrate our approach on publicly available SDSS data. We extract the most important features of the SDSS sample via principal component analysis. Next, we construct our model based on perturbations of a fixed base profile, ensuring that it captures these features. We then train a Convolutional Neural Network to estimate the free parameters of the model from noisy images of the PSF. This allows us to render a model image of each star, which we compare to the SDSS stars to evaluate the performance of our method. We find that our approach is able to accurately reproduce the SDSS PSF at the pixel level, which, due to the speed of both the model evaluation and the parameter estimation, offers good prospects for incorporating our method into the $MCCL$ framework.
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