Deep learning methods for obtaining photometric redshift estimations from images

Abstract

ABSTRACT Knowing the redshift of galaxies is one of the first requirements of many cosmological experiments, and as it is impossible to perform spectroscopy for every galaxy being observed, photometric redshift (photo-z) estimations are still of particular interest. Here, we investigate different deep learning methods for obtaining photo-z estimates directly from images, comparing these with ‘traditional’ machine learning algorithms which make use of magnitudes retrieved through photometry. As well as testing a convolutional neural network (CNN) and inception-module CNN, we introduce a novel mixed-input model that allows for both images and magnitude data to be used in the same model as a way of further improving the estimated redshifts. We also perform benchmarking as a way of demonstrating the performance and scalability of the different algorithms. The data used in the study comes entirely from the Sloan Digital Sky Survey (SDSS) from which 1 million galaxies were used, each having 5-filtre (ugriz) images with complete photometry and a spectroscopic redshift which was taken as the ground truth. The mixed-input inception CNN achieved a mean squared error (MSE) =0.009, which was a significant improvement ($30{{\ \rm per\ cent}}$) over the traditional random forest (RF), and the model performed even better at lower redshifts achieving a MSE = 0.0007 (a $50{{\ \rm per\ cent}}$ improvement over the RF) in the range of z < 0.3. This method could be hugely beneficial to upcoming surveys, such as Euclid and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), which will require vast numbers of photo-z estimates produced as quickly and accurately as possible.