From Observation to Ground Truth: Reconstruction Losses of Galaxy Imaging Under Heteroscedastic Noise

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 ${\chi }^2$ 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 $\text{textsc}GalaxyGenius$, 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 ${\chi }^2$-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.