Abstract:
   Galaxy image translation refers to a process that maps galaxy images from a source domain to a target domain, which is an important application in galaxy physics and cosmology.  With deep learning-based generative models, image translation has been performed for galaxy image generation, data quality enhancement, information extraction, and generalized for other tasks such as deblending and anomaly detection. However, most endeavors on image translation primarily focus on the pixel-level and morphology-level statistics of galaxy images. There is a lack of discussion on the preservation of more complex and higher-level physical information, which would be more challenging but crucial for studies that rely on high-fidelity data. Indeed, our investigation, using SDSS and CFHTLS paired galaxy images, illustrates that a few representative and conventionally trained translation models show different levels of incapabilities in retaining physical information (represented by spectroscopic redshift). To address this issue, we develop a model training approach that is both physically motivated and equipped with probabilistic modeling. In specific, galaxy images are reframed in a gradient space rather than in the conventional pixel space; that is, the log flux gradients along spatial and passband dimensions (equivalently, spatially resolved SEDs) are used in the training objective. Secondly, the weight of each gradient element in the training objective is adaptively estimated via probabilistic modeling (using normalizing flows). Our approach results in a translation model that is better aware of the color gradients of galaxies (or spatially resolved colors) compared to benchmark methods, automatically distinguishes between galaxy populations, and shows robustness against data scarcity. In particular, the preservation of redshift information can be improved by at least 40% relative to the baseline, and by 80% if spectroscopic information is further added in the input, as quantified by the redshift estimation uncertainties. This work is one of our attempts towards developing reliable data-driven and physics-aware models for scientific use.