Spectrum extraction from slitless spectrographic images

Motivated by the data analysis needs emerging from the ESA's cosmological mission Euclid, a linear noiseless model is introduced for a grism-generated slitless spectrographic image. A first-attempt strategy to spectrum deconvolution and decontamination is then suggested, neglecting the typical errors affecting this type of data, while trying to control the severe ill-posedness of the original problem. Three standard approaches are applied on a toy photometry, in order to have an idea on the solutions to be expected: the Moore-Penrose pseudoinversion, the standard Tikhonov regularization, and the preconditioned-projected Landweber iterative method.