Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model

International audienceThis paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies

Hybrid spectral unmixing : using artificial neural networks for linear/non-linear switching

Spectral unmixing is a key process in identifying spectral signature of materials and quantifying their spatial distribution over an image. The linear model is expected to provide acceptable results when two assumptions are satisfied: (1) The mixing process should occur at macroscopic level and (2) Photons must interact with single material before reaching the sensor. However, these assumptions do not always hold and more complex nonlinear models are required. This study proposes a new hybrid method for switching between linear and nonlinear spectral unmixing of hyperspectral data based on artificial neural networks. The neural networks was trained with parameters within a window of the pixel under consideration. These parameters are computed to represent the diversity of the neighboring pixels and are based on the Spectral Angular Distance, Covariance and a non linearity parameter. The endmembers were extracted using Vertex Component Analysis while the abundances were estimated using the method identified by the neural networks (Vertex Component Analysis, Fully Constraint Least Square Method, Polynomial Post Nonlinear Mixing Model or Generalized Bilinear Model). Results show that the hybrid method performs better than each of the individual techniques with high overall accuracy, while the abundance estimation error is significantly lower than that obtained using the individual methods. Experiments on both synthetic dataset and real hyperspectral images demonstrated that the proposed hybrid switch method is efficient for solving spectral unmixing of hyperspectral images as compared to individual algorithms

Hydrocarbon quantification using neural networks and deep learning based hyperspectral unmixing

Hydrocarbon (HC) spills are a global issue, which can seriously impact human life and the environment, therefore early identification and remedial measures taken at an early stage are important. Thus, current research efforts aim at remotely quantifying incipient quantities of HC mixed with soils. The increased spectral and spatial resolution of hyperspectral sensors has opened ground-breaking perspectives in many industries including remote inspection of large areas and the environment. The use of subpixel detection algorithms, and in particular the use of the mixture models, has been identified as a future advance that needs to be incorporated in remote sensing. However, there are some challenging tasks since the spectral signatures of the targets of interest may not be immediately available. Moreover, real time processing and analysis is required to support fast decision-making. Progressing in this direction, this thesis pioneers and researches novel methodologies for HC quantification capable of exceeding the limitations of existing systems in terms of reduced cost and processing time with improved accuracy. Therefore the goal of this research is to develop, implement and test different methods for improving HC detection and quantification using spectral unmixing and machine learning. An efficient hybrid switch method employing neural networks and hyperspectral is proposed and investigated. This robust method switches between state of the art hyperspectral unmixing linear and nonlinear models, respectively. This procedure is well suited for the quantification of small quantities of substances within a pixel with high accuracy as the most appropriate model is employed. Central to the proposed approach is a novel method for extracting parameters to characterise the non-linearity of the data. These parameters are fed into a feedforward neural network which decides in a pixel by pixel fashion which model is more suitable. The quantification process is fully automated by applying further classification techniques to the acquired hyperspectral images. A deep learning neural network model is designed for the quantification of HC quantities mixed with soils. A three-term backpropagation algorithm with dropout is proposed to avoid overfitting and reduce the computational complexity of the model. The above methods have been evaluated using classical repository datasets from the literature and a laboratory controlled dataset. For that, an experimental procedure has been designed to produce a labelled dataset. The data was obtained by mixing and homogenizing different soil types with HC substances, respectively and measuring the reflectance with a hyperspectral sensor. Findings from the research study reveal that the two proposed models have high performance, they are suitable for the detection and quantification of HC mixed with soils, and surpass existing methods. Improvements in sensitivity, accuracy, computational time are achieved. Thus, the proposed approaches can be used to detect HC spills at an early stage in order to mitigate significant pollution from the spill areas