Positivity-based separation of stellar spectra using a parametric mixing model

This article presents a method to extract stellar spectra from hyperspectral images of the MUSE instrument. Because of the MUSE PSF (Point Spread Function) effect, stars are not seen as dots but spread with a certain radius. In dense fields, the information in a pixel can thus result from contributions of different stars, which requires the use of a source separation method. We first derive the mixing model using known information about the MUSE PSF, then propose a source separation method using a parametric model of the spatial PSF, the FSF (Field Spread Function). Our method is based on the positivity of the data, sources and FSF parameters. It alternately estimates the star spectra, using a least square method with positivity constraints, and the FSF parameters by a projected gradient descent algorithm. Very satisfactory results are obtained with simulated but realistic MUSE data.