Beyond Colors: Probing Redshifts from Galaxy Morphology in Single-band Images with ViT-MDNz
To address the challenge of estimating redshifts when only single-band images are available, this study introduces a deep learning model named ViT-MDNz. Leveraging robust statistical priors learned from large-scale data concerning the correlation between redshift and morphology, the model can directly estimate redshifts and their associated uncertainties from single-band galaxy images. It integrates a Vision Transformer (ViT) to extract deep morphological features and a Mixture Density Network (MDN) to predict the full redshift probability density function. Trained and evaluated on approximately 300,000 single-band images from the DESI Legacy Imaging Surveys (DESI-LS), the model achieves a normalized median absolute deviation $\sigma_{\rm NMAD} = 0.034$ and an outlier fraction $f_{\rm out} = 2.6\%$ in the $r$-band for redshifts up to $z \lesssim 1$. Evaluations using probability integral transform (PIT) and continuous ranked probability score (CRPS) confirm that the predicted probability density functions are well calibrated and closely match the true distribution. These results demonstrate that competitive redshift estimates can be obtained using morphological features alone, and that incorporating color information further enhances the accuracy and robustness of the estimation. Therefore, ViT-MDNz provides a practical approach for redshift estimation of galaxy samples with limited photometric band coverage, contributing to improved completeness and usability of redshift catalogs for future large-scale surveys such as DESI and LSST.