Fourier Domain Approach for Galaxy Spectra Decontamination and Deconvolution

This article introduces a new method for decontaminating galaxy spectra within the framework of the Euclid space mission. Unlike our previously proposed methods that rely on a linear instantaneous model, this new method is based on a more realistic convolutive model. This model enables simultaneous decontamination and deconvolution of spectra, resulting in improved decontamination performance. First, we present a mixing model for observed data provided by four dispersion directions of light, transformed into the Fourier domain. Then, a method is proposed for estimating the spectrum of the object of interest. The effectiveness of the proposed method is demonstrated through preliminary results obtained using realistic noisy data.