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.

翻译：研究目的：本研究旨在探究U-Net架构是否能在无需点扩散函数（PSF）或噪声特性先验知识的情况下，独立完成天文图像的端到端盲反卷积处理。我们的目标是通过不同规模的训练图像集评估其性能，并与经典Tikhonov反卷积方法进行对比，同时检验其在变化的大气视宁度与噪声水平下的泛化能力。研究方法：使用GalSim工具包模拟真实天文观测数据，通过随机变换、PSF卷积（综合考虑光学与大气效应）及高斯白噪声构建数据集。基于COSMOS真实星系数据集，采用均方误差（MSE）损失函数对U-Net模型进行训练，训练集规模最大达40,000张48×48像素图像。使用峰值信噪比（PSNR）、结构相似性指数（SSIM）及余弦相似度指标评估性能，其中余弦相似度通过双模型框架用于评估解稳定性。研究结果：U-Net模型在盲反卷积任务中表现有效，其性能随训练数据量增加持续提升，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间解趋于收敛，表明解具有稳定性。值得注意的是，在挑战性条件（低PSNR/中等SSIM）下，U-Net表现优于类先知Tikhonov方法。该模型对未参与训练的视宁度与噪声条件也展现出良好泛化能力，但当训练参数包含验证条件时能达到最优性能。在合成$C^α$图像上的实验进一步支持以下假设：U-Net学习到的是几何自适应调和基，类似于去噪任务中观察到的稀疏表示。这些结果与近期关于其自适应学习能力的数学见解相一致。