A method based on spatial and spectral information to reduce the solution space in endmember extraction algorithms

Abstract

Spectral unmixing is a widely used approach for analysing hyperspectral images. This technique requires the knowledge of endmember spectral signatures that are commonly extracted from the observed data. Unfortunately, the computational complexity of current endmember extraction methods scales linearly with the number of pixels, which typically consists of the entire data set. In this paper, we propose a method to reduce the solution space for geometry-based endmember extraction algorithms. The nearest spectrum to the average spectra enclosed in non-overlapping windows is first selected. In the signal subspace, these spectra are located close to or at the centre of the data cloud enclosed within their respective window. We argue that, excepted for some peculiar situations, these local near-central (LNC) spectra cannot belong to data vertices where endmembers are expected to reside. We exploit this property to identify a set of LNC spectra endmembers defining a simplex inscribed within the true endmember simplex. The simplex is determined using the N-FINDR algorithm. Spectra that are located outside the simplex defined by these LNC spectra endmembers represent the reduced pool of potential endmembers. Comparison with state-of-the-art techniques on synthetic and real hyperspectral data indicates that the proposed method provides equal or better levels of performance while maintaining good efficiency in terms of execution times.