Semi-blind separation of galaxy spectra from a mixture obtained by slitless spectroscopy

We investigate the problem of separating galaxy spectra from their mixtures resulting from the slitless spectroscopy used in the future Euclid space mission. This can be formulated as a source separation problem where the structure of the mixture is specific and depends on a low number of parameters. We first develop a mathematical model to describe the observations generated by the near-infrared spectrograph of Euclid, then propose non-blind, semi-blind and regularized semi-blind methods to separate the spectra. The first simulation results are encouraging: even for a signal to noise ratio of 5 dB, our regularized semi-blind method succeeds in separating the considered two spectra and provides a satisfactory estimate of the emission line positions and amplitudes.