From Observation to Ground Truth: Reconstruction Losses of Galaxy Imaging Under Heteroscedastic Noise
Abstract
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 χ2 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 χ2-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.
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BibTeX
@misc{ye2026from,
title = {{From Observation to Ground Truth: Reconstruction Losses of Galaxy Imaging Under Heteroscedastic Noise}},
author = {Renhao Ye and Shiyin Shen and Quanfeng Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21350},
eprint = {2609.21350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21350},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Observation to Ground Truth: Reconstruction Losses of Galaxy Imaging Under Heteroscedastic Noise
AU - Renhao Ye
AU - Shiyin Shen
AU - Quanfeng Xu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21350
UR - https://arxiv.org/abs/2609.21350
AB - 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.
ER -