On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Abstract

The surface of Mars is currently being imaged with an unprecedented combination of spectral and spatial resolution. This high resolution, and its spectral range, give the ability to pinpoint chemical species on the surface and the atmosphere of Mars moreaccurately than before. The subject of this paper is to present a method to extract informations on these chemicals from hyperspectral images. A first approach, based on Independent Component Analysis (ICA) [1], is able to extract artifacts and locations of CO2 and H2O ices. However, the main independence assumption and some basic properties (like the positivity of images and spectra) being unverified, the reliability of all the independent components (ICs) is weak. For improving the component extraction and consequently the endmember classification, a combination of spatial ICA with spectral Bayesian Positive Source Separation (BPSS) [2] is proposed. To reduce the computational burden, the basic idea is to use spatial ICA yielding a rough classification of pixels, which allows selection of small, but relevant, number of pixels and then BPSS is applied for the estimation of the source spectra using the spectral mixtures provided by this reduced set of pixels. Finally, the abundances of the components is assessed on the whole pixels of the images. Results of this approach are shown and evaluated by comparison with available reference spectra.

Extraction of minerals on the south pole of the planet Mars by unsupervised linear unmixing of hyperspectral images

“…Based on the spectra extracted by VCA, SISAL and MVC-NMF, the abundance maps are computed by using UCLS, NCLS and FCLS. They are compared with the abundances obtained by the state-of-art unmixing method BPSS presented in [2]. In Section 2.4, another comparison is performed this time on a restricted area with the reference abundances obtained in [12] by inversion of a physical model.…”

“…For this purpose, PCA-based thresholding can be used [2]. However, the cut-off threshold is not easy to determine since the eingenvalues caused by the signals and noise are sometimes very similar.…”

“…For this purpose, one can find three types of approaches: (i) statistical methods (ii) geometrical methods and (iii) non negative matrix factorization (NMF) methods. The statistical methods -such as the Independent Component Analysis (ICA) [6] and Bayesian Positive Source Separation (BPSS) [7] -extract the endmembers by optimizing some statistical criteria, for example the independence between the endmembers, which is assumed by ICA. However, either the statistical criteria are not always valid for planetary hyperspectral images or the statistical methods, such as BPSS, which performs Monte-Carlo simulations for obtaining the endmembers, are extremely slow.…”

Minimum Volume Simplex Analysis: A Fast Algorithm to Unmix Hyperspectral Data

“…Accorging to the Bayes law, the posterior includes two factors: the observation density, which may account for additive noise, and a prior, which may impose constraints on the endmember matrix (e.g., nonnegativity of its elements) and on the abundance fractions (e.g., to be in the probability simplex) and model spectral variability. Works [8,9] are representative of this line of attack.…”

Fast Constrained Least Squares Spectral Unmixing Using Primal-Dual Interior-Point Optimization

“…Then, the remaining step of the unmixing is the estimation of the fractional abundances. Actually, there is an increasing interest to joint estimation methods based either on non-negative source separation [5,6] or constrained non-negative matrix factorization [7,8]. However, the purpose of this paper is to focus on the second step of the supervised approach with the aim to present a fast computation method adapted to the case of large data sets.…”