An Augmented Perturbed Linear Mixing Model with Scaling Factors for Unmixing

Due to different illumination conditions, complex atmospheric conditions and other reasons, the endmember spectral profile of the same feature shows visible variation at different locations in the hyperspectral image, a phenomenon known as the endmember spectral variability (ESV). The identified endmembers can be considered as changeable instances of reference endmembers, and it can be better constructed by scaling factors and perturbation. The scaling factors are suitable for constructing equal proportional changes and the perturbation can construct non-proportional changes. To address the problem that spectral variability is difficult to be constructed by perturbation or scaling factors alone, the article proposes an augmented perturbed linear mixing model (APLMM) by adding scaling factors on the perturbed linear mixing model (PLMM). The APLMM aims at incorporating spectral variability in the hyperspectral unmixing under the form of equal proportional and non-proportional changes of endmembers. In addition, to control the strength of the equal proportional changes, the article adds penalty terms for the scaling factors to the model. We use the alternating direction method of multipliers (ADMM) to optimise the variables in the APLMM algorithm. Experimental results on synthetic and real datasets demonstrate the effectiveness of the proposed model.

I. Introduction

Hyperspectral image processing and information extraction technology is one of the core research elements in the field of hyperspectral remote sensing [1]. Hyperspectral images have a larger number of bands and contain more spectral information, but the processing of hyperspectral images can also become more complex [2]. A pixel is called a pure pixel or endmembers if it contains only one material, and a mixed pixel if it contains more than one material [3]. Hyperspectral unmixing is a common form of data processing performed on hyperspectral images, and it decomposes the hyperspectral image into the endmember matrix and the abundance matrix [4]–[7].