Unmixing methods based on nonnegativity and weakly mixed pixels for astronomical hyperspectral datasets

An increasing number of astronomical instruments (on Earth and space-based) provide hyperspectral images, that is three-dimensional data cubes with two spatial dimensions and one spectral dimension. The intrinsic limitation in spatial resolution of these instruments implies that the spectra associated with pixels of such images are most often mixtures of the spectra of the "pure" components that exist in the considered region. In order to estimate the spectra and spatial abundances of these pure components, we here propose an original blind signal separation (BSS), that is to say an unsupervised unmixing method. Our approach is based on extensions and combinations of linear BSS methods that belong to two major classes of methods, namely nonnegative matrix factorization (NMF) and sparse component analysis (SCA). The former performs the decomposition of hyperspectral images, as a set of pure spectra and abundance maps, by using nonnegativity constraints, but the estimated solution is not unique: It highly depends on the initialization of the algorithm. The considered SCA methods are based on the assumption of the existence of points or tiny spatial zones where only one source is active (i.e., one pure component is present). These points or zones are then used to estimate the mixture and perform the decomposition. In real conditions, the assumption of perfect single-source points or zones is not always realistic. In such conditions, SCA yields approximate versions of the unknown sources and mixing coefficients. We propose to use part of these preliminary estimates from the SCA to initialize several runs of the NMF in order to refine these estimates and further constrain the convergence of the NMF algorithm. The proposed methods also estimate the number of pure components involved in the data and they provide error bars associated with the obtained solution. Detailed tests with synthetic data show that the decomposition achieved with such hybrid methods is nearly unique and provides good performance, illustrating the potential of applications to real data.