Estimating Nonlinearities in p-Linear Hyperspectral Mixtures

Accurately estimating the elements in Earth observations is crucial when assessing specific features such as air quality index, water pollution, or urbanization process behavior. Moreover, physical-chemical composition can be retrieved from hyperspectral images when proper spectral unmixing architectures are employed. Specifically, when linear and nonlinear combinations of endmembers (pure spectral components) are accurately characterized, hyperspectral unmixing plays a key role in understanding and quantifying phenomena occurring over the instantaneous field-of-view. Thus, reliable detection of nonlinear reflectance behavior can play a key role in enhancing hyperspectral unmixing performance. In this paper, two new methods for adaptive design of mixture models for hyperspectral unmixing are introduced. One of the methods relies on exploiting geometrical features of hyperspectral signatures in terms of nonorthogonal projections onto the space induced by the endmembers' spectra. Then, an iterative process aims at understanding the order of local nonlinearity that is displayed by each endmember over every pixel. An improved version of an artificial neural network-based approach for nonlinearity order information is also considered and compared. Experimental results show that the proposed approaches are actually able to retrieve thorough information on the nature of the nonlinear effects over the image, while providing excellent performance in reconstructing the given data sets.

I. Introduction

Hyperspectral imagery provides a huge amount of information about spectral features of the earth surface [1]–[8]. Specifically, physical composition and anthropogenic phenomena (such as urbanization processes, air pollution, and water quality and distribution [9], [10]) can be detailed by appropriately estimating the fractions of the materials and elements (endmembers) appearing at each location [11].