The hyperspectral imagery provides images in hundreds of spectral bands within different wavelength regions. This technology has increasingly applied in different fields of earth sciences, such as minerals exploration, environmental monitoring, agriculture, urban science, and planetary remote sensing. However, despite the ability of these data to detect surface features, the measured spectrum is composed of several components that make it a mixed spectrum due to the low spatial resolution observed of the employed sensors or the presence of multiple materials in its instantaneous field of view (IFOV). The existence of a mixed spectrum severely prevents the accurate processing of the hyperspectral data. Therefore, it is necessary to separate these mixtures through the so-called spectral unmixing methods. Spectral unmixing is performed to decompose a mixed pixel in hyperspectral images into a set of spectra (endmembers) and their abundances. Typically, two types of spectral mixing models (linear and nonlinear) are considered. In the linear mixing model (LMM), the reflected radiance at the sensor is the outcome of interference with one material, where a pixel is assumed to be a linear combination of endmembers weighted by their abundances. The nonlinear model, on the other hand, is used when the mixing scale is microscopic or materials are mixed intrinsically. In recent years, the linear mixing model has been a very popular model for hyperspectral processing in the last decades, and a large effort has been put into using this model for unmixing applications, resulting in an overabundance of linear unmixing methods and algorithms. Over the last decades, the linear mixing model has been utilized in the detection of minerals and their abundances. However, as early as 40 years ago, it has been observed that strong nonlinear spectral mixing effects are present in many situations, for instance, when there are multi scattering effects or intimate mineral interactions. While such nonlinear unmixing techniques have received much less attention than linear ones.
Therefore, this paper aims to give an overview of the majority of nonlinear mixing models and methods used in hyperspectral image processing, and many recent developments in this ﬁeld. Besides, several of the more popular nonlinear unmixing techniques are explained in detail. In this regard, nonlinear unmixing methods can be categorized into two groups: physics-based methods and data-driven techniques. The most important methods of these two groups are divided into bilinear and multi-linear models, intimate mineral mixture models, radiosity based approaches, ray tracing, neural network, kernel methods, manifold learning, and topology methods. A comprehensive review of these methods can be found in which bilinear and multi-linear models and neural networks have become more popular among researchers over the years. The current study should give the reader that is interested in working with nonlinear unmixing techniques a reasonably good introduction into the most commonly used methods and approaches.