Generalization of Subpixel Analysis for Hyperspectral Data With Flexibility in Spectral Similarity Measures

Several spectral unmixing techniques have been developed for subpixel mapping using hyperspectral data in the past two decades, among which the fully constrained least squares method based on the linear spectral mixture model (LSMM) has been widely accepted. However, the shortage of this method is that the Euclidean spectral distance measure is used, and therefore, it is sensitive to the magnitude of the spectra. While other spectral matching criteria are available, such as spectral angle mapping (SAM) and spectral information divergence (SID), the current unmixing algorithm is unable to be extended to these measures. In this paper, we propose a unified subpixel mapping framework that models the unmixing process as a best match of the unknown pixel´s spectrum to a weighted sum of the endmembers´ spectra. We introduce sequential quadratic programming to solve the nonlinear optimization problem encountered in the implementation of this framework. The main feature of this proposed method is that it is not restricted to any particular similarity measures. Experiments were conducted with both simulated and Hyperion data. The tests demonstrated the proposed framework´s advantage in accommodating various spectral similarity measures and provided performance comparisons of the Euclidean distance measure with other spectral matching criteria including SAM, spectral correlation measure, and SID.