Blind decomposition of Herschel-HIFI spectral maps of the NGC 7023 nebula

Large spatial-spectral surveys are more and more common in astronomy. This calls for the need of new methods to analyze such mega- to giga-pixel data-cubes. In this paper we present a method to decompose such observations into a limited and comprehensive set of components. The original data can then be interpreted in terms of linear combinations of these components. The method uses non-negative matrix factorization (NMF) to extract latent spectral end-members in the data. The number of needed end-members is estimated based on the level of noise in the data. A Monte-Carlo scheme is adopted to estimate the optimal end-members, and their standard deviations. Finally, the maps of linear coefficients are reconstructed using non-negative least squares. We apply this method to a set of hyperspectral data of the NGC 7023 nebula, obtained recently with the HIFI instrument onboard the Herschel space observatory, and provide a first interpretation of the results in terms of 3-dimensional dynamical structure of the region.