AI 中文总结
本研究通过模拟星系图像比较三种重构损失，发现逆方差加权χ²损失在异方差噪声下优于MSE和MAE，能更准确地重构星系图像。
AI 中文摘要
深度学习被广泛用于分析星系图像，而重构损失决定了模型在训练过程中优先关注哪些图像特征。均方误差（MSE）和平均绝对误差（MAE）分别对应于同方差高斯似然和拉普拉斯似然，而逆方差加权的χ²损失则考虑了异方差天文噪声的空间变化不确定性。比较这些目标函数在多大程度上恢复潜在信号需要一个真值（GT），而真实观测无法提供这一真值。因此，我们使用IllustrisTNG、SKIRT和GalaxyGenius生成无噪声星系图像，将其与点扩散函数（PSF）卷积以定义真值，并构建带噪声的模拟观测。我们使用三种重构损失训练其他方面完全相同的变分自编码器（VAEs），并评估其输出与真值的差异。在评估的大多数信噪比（SNR）范围内，χ²训练模型产生的相对重构误差低于MSE和MAE训练模型，表明在此考虑的异方差噪声下，逆方差加权改善了星系图像重构。
英文摘要
Deep learning is widely used to analyze galaxy images, and the reconstruction loss determines which image features a model prioritizes during training. Mean squared error (MSE) and mean absolute error (MAE) correspond to homoscedastic Gaussian and Laplace likelihoods, respectively, whereas the inverse-variance-weighted $χ^2$ loss accounts for the spatially varying uncertainties of heteroscedastic astronomical noise. Comparing how closely these objectives recover the underlying signal requires a ground truth (GT), which real observations cannot provide. We therefore generate noise-free galaxy images with IllustrisTNG, SKIRT, and \textsc{GalaxyGenius}, convolve them with a point-spread function (PSF) to define the GT, and construct noisy simulated observations. We train otherwise identical variational autoencoders (VAEs) with the three reconstruction losses and evaluate their outputs against the GT. Over most of the evaluated signal-to-noise ratio (SNR) range, the $χ^2$-trained model yields lower relative reconstruction errors than the MSE- and MAE-trained models, indicating that inverse-variance weighting improves galaxy-image reconstruction under the heteroscedastic noise considered here.
Comments15 pages, 9 figures, accepted by Universe, Special Issue: New Discoveries in Astronomical Data (II)
