A new unsupervised method for hyperspectral image unmixing using a linear-quadratic model

This paper deals with pixel unmixing in hyperspectral remote sensing images. The surface covered by one pixel of these images may contain more than one material component. Thus, the spectrum obtained from such a pixel may result from different contributions of several materials. Using a blind source separation (BSS) method, we aim at decomposing each mixed pixel spectrum into several pure material spectra and their relative contributions. Due to the non-flat landscape, for example in urban areas, the resulting spectrum is obtained from reflections between the various surfaces. As a result, the classical linear mixing model, generally used in BSS methods, is no longer valid. In this work, we propose a new non-linear unmixing method for hyperspectral remote sensing images using a linear-quadratic model. Our approach starts by estimating the number of pure materials called endmembers. Then, supposing the existence of at least two pure pixels per material in the image, it achieves source separation by going through the following stages: endmember spectra estimation, classification into clusters, and estimation of abundance and reflection fractions. Experimental results on artificial mixtures of real spectra confirm the effectiveness of the proposed method.