Photometric redshifts from SDSS images using a convolutional neural network

We developed a deep convolutional neural network (CNN), used as a classifier, to estimate photometric redshifts and associated probability distribution functions (PDF) for galaxies in the Main Galaxy Sample of the Sloan Digital Sky Survey at z < 0.4. Our method exploits all the information present in the images without any feature extraction. The input data consist of 64 x 64 pixel ugriz images centered on the spectroscopic targets, plus the galactic reddening value on the line-of-sight. For training sets of 100k objects or more (>= 20% of the database), we reach a dispersion sigma(MAD) < 0.01, significantly lower than the current best one obtained from another machine learning technique on the same sample. The bias is lower than 10(-4), independent of photometric redshift. The PDFs are shown to have very good predictive power. We also find that the CNN redshifts are unbiased with respect to galaxy inclination, and that sigma(MAD) decreases with the signal-to-noise ratio (S/N), achieving values below 0.007 for S/N > 100, as in the deep stacked region of Stripe 82. We argue that for most galaxies the precision is limited by the S/N of SDSS images rather than by the method. The success of this experiment at low redshift opens promising perspectives for upcoming surveys.