天文学中的盲去卷积：独立U-Net性能如何？
Blind Deconvolution in Astronomy: How Does a Standalone U-Net Perform?
AI总结：
本研究评估了U-Net在天文图像盲去卷积中的性能，发现其在不同观测和噪声条件下表现优异，优于传统方法。
摘要：
目标：本研究探讨U-Net架构是否能独立端到端地进行天文图像的盲去卷积，而无需任何点扩散函数（PSF）或噪声特征的先验知识。我们的目标是评估其在训练图像数量、经典Tikhonov去卷积以及不同观测条件和噪声水平下的泛化能力。 方法：使用GalSim工具包模拟现实天文观测，包括随机变换、PSF卷积（考虑光学和大气效应）以及高斯白噪声。使用均方误差（MSE）损失函数在不同大小的数据集上训练U-Net模型，数据集大小最多达到40,000张48x48的COSMOS真实星系数据集。使用PSNR、SSIM和余弦相似度指标进行评估，后者在双模型框架中用于评估解的稳定性。 结果：U-Net模型在盲去卷积中表现出色，随着训练数据集大小的增加，性能持续改善，在超过5,000张图像后趋于饱和。余弦相似度分析显示独立训练模型之间收敛，表明解的稳定。令人印象深刻的是，U-Net在挑战性条件下（低PSNR/中等SSIM）优于类似Oracle的Tikhonov方法。该模型在未见过的观测和噪声条件下泛化良好，尽管当训练参数包含验证条件时才能获得最佳性能。对合成$C^α$图像的实验进一步支持了假设，即U-Net学习了一种几何自适应的谐波基，类似于去噪任务中观察到的稀疏表示。这些结果与最近关于其自适应学习能力的数学见解相一致。
英文摘要：
Aims: This study investigates whether a U-Net architecture can perform standalone end-to-end blind deconvolution of astronomical images without any prior knowledge of the Point Spread Function (PSF) or noise characteristics. Our goal is to evaluate its performance against the number of training images, classical Tikhonov deconvolution and to assess its generalization capability under varying seeing conditions and noise levels. Methods: Realistic astronomical observations are simulated using the GalSim toolkit, incorporating random transformations, PSF convolution (accounting for both optical and atmospheric effects), and Gaussian white noise. A U-Net model is trained using a Mean Square Error (MSE) loss function on datasets of varying sizes, up to 40,000 images of size 48x48 from the COSMOS Real Galaxy Dataset. Performance is evaluated using PSNR, SSIM, and cosine similarity metrics, with the latter employed in a two-model framework to assess solution stability. Results: The U-Net model demonstrates effectiveness in blind deconvolution, with performance improving consistently as the training dataset size increases, saturating beyond 5,000 images. Cosine similarity analysis reveals convergence between independently trained models, indicating stable solutions. Remarkably, the U-Net outperforms the oracle-like Tikhonov method in challenging conditions (low PSNR/medium SSIM). The model also generalizes well to unseen seeing and noise conditions, although optimal performance is achieved when training parameters include validation conditions. Experiments on synthetic $C^α$ images further support the hypothesis that the U-Net learns a geometry-adaptive harmonic basis, akin to sparse representations observed in denoising tasks. These results align with recent mathematical insights into its adaptive learning capabilities.
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