Separation of stellar spectra from hyperspectral images using particle filtering constrained by a parametric spatial mixing model

In a hyperspectral image of a dense stellar field, each pixel is a mixture of contributions from the star spectra. Indeed, because of the data acquisition system, each star spectrum is spread out over several pixels, which is modeled by the PSF (point spread function). The objective of our work is to develop a method to separate star spectra. The star spectra can be highly correlated and are not sparse. Therefore, the classical blind source separation (BSS) methods based on Independent Component Analysis (ICA) or spectral sparsity are not appropriate to solve this problem. On the other hand, methods based on Non-negative Matrix Factorisation (NMF) are sensitive to the initialization and can´t account for a particular structure of the mixing matrix. In this paper, we propose to solve this problem with a Sequential Bayesian method (particle filter). This method is based on a hidden Markov model in which we take into account the particular structure of the mixing matrix (PSF model), prior information about the PSF parameters and star positions but do not use prior information concerning the spectra. The results obtained on a realistic simulated scenario are very encouraging.