Denoising galaxy spectra with coupled dictionary learning

The Euclid satellite aims to measure accurately the global properties of the Universe, with particular emphasis on the properties of the mysterious Dark Energy that is driving the acceleration of its expansion. One of its two main observational probes relies on accurate measurements of the radial distances of galaxies through the identification of important features in their individual light spectra that are redshifted due to their receding velocity. However, several challenges for robust automated spectroscopic redshift estimation remain unsolved, one of which is the characterization of the types of spectra present in the observed galaxy population. This paper proposes a denoising technique that exploits the mathematical frameworks of Sparse Representations and Coupled Dictionary Learning, and tests it on simulated Euclid-like noisy spectroscopic templates. The reconstructed spectral profiles are able to improve the accuracy, reliability and robustness of automated redshift estimation methods. The key contribution of this work is the design of a novel model which considers coupled feature spaces, composed of high- and low-quality spectral profiles, when applied to the spectroscopic data denoising problem. The coupled dictionary learning technique is formulated within the context of the Alternating Direction Method of Multipliers, optimizing each variable via closed-form expressions. Experimental results suggest that the proposed powerful coupled dictionary learning scheme reconstructs successfully spectral profiles from their corresponding noisy versions, even with extreme noise scenarios.