  In high-energy astronomy, spectro-imaging instruments such as X-ray detectors
allow investigation of the spatial and spectral properties of extended sources
including galaxy clusters, galaxies, diffuse interstellar medium, supernova
remnants and pulsar wind nebulae. In these sources, each physical component
possesses a different spatial and spectral signature, but the components are
entangled. Extracting the intrinsic spatial and spectral information of the
individual components from this data is a challenging task. Current analysis
methods do not fully exploit the 2D-1D (x,y,E) nature of the data, as the
spatial and spectral information are considered separately. Here we investigate
the application of a Blind Source Separation algorithm that jointly exploits
the spectral and spatial signatures of each component in order to disentangle
them. We explore the capabilities of a new BSS method (General Morphological
Component Analysis; GMCA), initially developed to extract an image of the
Cosmic Microwave Background from Planck data, in an X-ray context. The
performance of GMCA on X-ray data is tested using Monte-Carlo simulations of
supernova remnant toy models, designed to represent typical science cases. We
find that GMCA is able to separate highly entangled components in X-ray data
even in high contrast scenarios, and can extract with high accuracy the
spectrum and map of each physical component. A modification is proposed to
improve the spectral fidelity in the case of strongly overlapping spatial
components, and we investigate a resampling method to derive realistic
uncertainties associated to the results of the algorithm. Applying the modified
algorithm to the deep Chandra observations of Cassiopeia A, we are able to
produce detailed maps of the synchrotron emission at low energies (0.6-2.2
keV), and of the red/blue shifted distributions of a number of elements
including Si and Fe K.
