Nonlinear deconvolution of hyperspectral data with MCMC for studying the kinematics of galaxies

Hyperspectral imaging has been an area of active research in image processing and analysis for more than 10 years, mainly for remote sensing applications. Astronomical ground-based hyperspectral imagers offer new challenges to the community, which differ from the previous ones in the nature of the observed objects, but also in the quality of the data, with a low signal-to-noise ratio and a low resolution, due to the atmospheric turbulence. In this paper, we focus on a deconvolution problem specific to hyperspectral astronomical data, to improve the study of the kinematics of galaxies. The aim is to estimate the flux, the relative velocity, and the velocity dispersion, integrated along the line-of-sight, for each spatial pixel of an observed galaxy. Thanks to the Doppler effect, this is equivalent to estimate the amplitude, center, and width of spectral emission lines, in a small spectral range, for every spatial pixel of the hyperspectral data. We consider a parametric model for the spectral lines and propose to compute the posterior mean estimators, in a Bayesian framework, using Monte Carlo Markov chain algorithms. Various estimation schemes are proposed for this nonlinear deconvolution problem, taking advantage of the linearity of the model with respect to the flux parameters. We differentiate between methods taking into account the spatial blurring of the data (deconvolution) or not (estimation). The performances of the methods are compared with classical ones, on two simulated data sets. It is shown that the proposed deconvolution method significantly improves the resolution of the estimated kinematic parameters.