Implementation Strategies for Hyperspectral Unmixing Using Bayesian Source Separation

Abstract

Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has been so far limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy which allows one to apply these algorithms on a full hyperspectral image, as typical in Earth and Planetary Science, is introduced. Effects of pixel selection, the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different dataset have been used: a synthetic one and a real hyperspectral image from Mars.

HALS-based NMF with flexible constraints for hyperspectral unmixing

“…Some prior knowledge should be used to reduce the number of references before the comparison. (3) We use a linear mixing model in this article, but the radiative transfer is always nonlinear in real scene [10]. (4) It is subjective to identify the endmembers with SAD.…”

“…In these cases, the separation problem can be addressed in a Bayesian framework. Several Bayesian Positive Source Separation (BPSS) algorithms under positivity and sum-to-one constraints have recently been developed [8][9][10]. In [10], a discussion on the effectiveness of the sum-to-one constraint is given, showing that full constrained BPSS2 gives better results than BPSS for simulated data, while it is the contrary for the real OMEGA data, "due to nonlinearity in the radiative transfer and noise in the dataset in contradiction with the full additivity constraint".…”

“…Several Bayesian Positive Source Separation (BPSS) algorithms under positivity and sum-to-one constraints have recently been developed [8][9][10]. In [10], a discussion on the effectiveness of the sum-to-one constraint is given, showing that full constrained BPSS2 gives better results than BPSS for simulated data, while it is the contrary for the real OMEGA data, "due to nonlinearity in the radiative transfer and noise in the dataset in contradiction with the full additivity constraint". We think that it would be not the same with the proposed NMFbased algorithm, firstly because the full additivity is not a hard but a soft constraint, and second because the residual error RQE is able to represent measurement noise or model noise, and then the algorithm is quite robust for real data, which can contain nonlinear mixed terms.…”

Intercomparison and Validation of Techniques for Spectral Unmixing of Hyperspectral Images: A Planetary Case Study

“…In BPSS, the degree of uncertainty affecting the extracted endmember spectra can be estimated since results are computed as probability distribution functions. In [36], numerical schemes are devised to reduce the computation time which is a critical point of BPSS. This method has been applied satisfactorily on OMEGA hyperspectral images in [12] yet never on CRISM's.…”

Accuracy and performance of linear unmixing techniques for detecting minerals on OMEGA/Mars express

“…The R rows of the matrix S contain the surface pure spectra of the R components and each element a p,r of matrix A corresponds to the abundance of the r th component in the pixel p. The supervised linear unmixing problem consists of estimating matrix A knowing X and S, in contrary to unsupervised unmixing that consists of estimating matrix A and S, knowing only X [2]. A first strong constraint is the non-negativity of the elements of A since they correspond to abundances of the surface components:…”