Modeling linear and intimate mixtures of materials in hyperspectral imagery with single-scattering albedo and kernel approaches

Abstract. Linear mixtures of materials in a scene often occur because the resolution of a sensor is relatively coarse, resulting in pixels containing patches of different materials within them. This phenomenon causes nonoverlapping areal mixing and can be modeled by a linear mixture model. More complex phenomena, such as the multiple scattering in mixtures of vegetation, soils, granular, and microscopic materials within pixels can result in intimate mixing with varying degrees of nonlinear behavior. In such cases, a linear model is not sufficient. This study considers two approaches for unmixing pixels in a scene that may contain linear or intimate (nonlinear) mixtures. The first method is based on earlier studies that indicate nonlinear mixtures in reflectance space are approximately linear in albedo space. The method converts reflectance to single-scattering albedo according to Hapke theory and uses a constrained linear model on the computed albedo values. The second method is motivated by the same idea, but uses a kernel that seeks to capture the linear behavior of albedo in nonlinear mixtures of materials. This study compares the two approaches and pays particular attention to these dependencies. Both laboratory and airborne collections of hyperspectral imagery are used to validate the methods.