Hyperspectral Image Data Reduction for Endmember Extraction

Endmember extraction from hyperspectral images aims to identify the spectral signatures of materials present in a scene. Recent studies have shown that self-dictionary methods can achieve high extraction accuracy; however, their high computational cost limits their applicability to large-scale hyperspectral images. Although several approaches have been proposed to mitigate this issue, it remains a major challenge. Motivated by this situation, this paper pursues a data reduction approach. Assuming that a hyperspectral image follows the linear mixing model with the pure-pixel assumption, we develop a data reduction technique to remove pixels corresponding to mixtures of multiple endmember signatures. We analyze the theoretical properties of this reduction step and show that it preserves pixels that lie close to the endmembers. Building on this result, we propose a data-reduced self-dictionary method that integrates the data reduction with a self-dictionary method based on a linear programming formulation. Numerical experiments demonstrate that the proposed method can substantially reduce the computational time of the original self-dictionary method without sacrificing endmember extraction accuracy.