A Fast Endmember Estimation Algorithm from Compressive Measurements

This paper deals with estimating the endmembers in a linear mixing model (LMM) of a hyperspectral image, from measurements acquired with compressive spectral imaging (CSI) devices. For this problem, a novel approach is developed exploiting the Rayleigh-Ritz (RR) theory to approximate the signal subspace where the data lie and the fact that the endmembers are located at the vertices of a simplex set under a LMM. The proposed approach first estimates a subset of eigenvectors to approximate the signal subspace using the RR theory, and then vertex component analysis is applied to find the endmembers in the approximated subspace. Simulations results conducted on realistic compressive hyperspectral images show that the proposed algorithm can provide endmembers results very close to those obtained when using uncompressed images, with the advantage of using a reduced number of measurements. In particular, the numerical tests show that the proposed approach is able to estimate the endmembers using 50% of the full data.