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 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.

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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.

Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

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Hyperspectral Remote Sensing Data Analysis and Future Challenges

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

A Viking Lander 1 image was modeled as mixtures of reflectance spectra of palagonite dust, gray andesitelike rock, and a coarse rocklike soil. The rocks are covered to varying degrees by dust but otherwise appear unweathered. Rocklike soil occurs as lag deposits in deflation zones around stones and on top of a drift and as a layer in a trench dug by the lander. This soil probably is derived from the rocks by wind abrasion and/or spallation. Dust is the major component of the soil and covers most of the surface. The dust is unrelated spectrally to the rock but is equivalent to the global-scale dust observed telescopically. A new method was developed to model a multispectral image as mixtures of end-member spectra and to compare image spectra directly with laboratory reference spectra. The method for the first time uses shade and secondary illumination effects as spectral end-members; thus the effects of topography and illumination on all scales can be isolated or removed. The image was calibrated absolutely from the laboratory spectra, in close agreement with direct calibrations. The method has broad applications to interpreting multispectral images, including satellite images.

Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]

In hyperspectral unmixing, the prevalent model used is the linear mixing model, and a large variety of techniques based on this model has been proposed to obtain endmembers and their abundances in hyperspectral imagery. However, it has been known for some time that nonlinear spectral mixing effects can be a crucial component in many real-world scenarios, such as planetary remote sensing, intimate mineral mixtures, vegetation canopies, or urban scenes. While several nonlinear mixing models have been proposed decades ago, only recently there has been a proliferation of nonlinear unmixing models and techniques in the signal processing literature. This paper aims to give an historical overview of the majority of nonlinear mixing models and nonlinear unmixing methods, and to explain some of the more popular techniques in detail. The main models and techniques treated are bilinear models, models for intimate mineral mixtures, radiosity-based approaches, ray tracing, neural networks, kernel methods, support vector machine techniques, manifold learning methods, piece-wise linear techniques, and detection methods for nonlinearity. Furthermore, we provide an overview of several recent developments in the nonlinear unmixing literature that do not belong into any of these categories.

A Review of Nonlinear Hyperspectral Unmixing Methods

We present a new algorithm for linear spectral mixture analysis, which is capable of supervised unmixing of hyperspectral data while respecting the constraints on the abundance coefficients. This simplex-projection unmixing algorithm is based upon the equivalence of the fully constrained least squares problem and the problem of projecting a point onto a simplex. We introduce several geometrical properties of high-dimensional simplices and combine them to yield a recursive algorithm for solving the simplex-projection problem. A concrete implementation of the algorithm for large data sets is provided, and the algorithm is benchmarked against well-known fully constrained least squares unmixing (FCLSU) techniques, on both artificial data sets and real hyperspectral data collected over the Cuprite mining region. Unlike previous algorithms for FCLSU, the presented algorithm possesses no optimization steps and is completely analytical, severely reducing the required processing power.

Fully Constrained Least Squares Spectral Unmixing by Simplex Projection

In hyperspectral unmixing, bilinear and linear–quadratic models have become popular recently, and also the polynomial postnonlinear model shows promising results. These models do not consider endmember interactions involving more than two endmembers, although such interactions might compose a nontrivial part of the observed spectrum in scenarios involving bright materials and complex geometrical structures, such as vegetation and intimate mixtures. In this paper, we present an extension of these models to include an infinite number of interactions. Several technical problems, such as divergence of the resulting series, can be avoided by introducing an optical interaction probability, which becomes the only free parameter of the model in addition to the abundances. We present an unmixing strategy based on this multilinear mixing (MLM) model; present comparisons with the bilinear models and the Hapke model for intimate mixing; and show that, in several scenarios, the MLM model obtains superior results.

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A Multilinear Mixing Model for Nonlinear Spectral Unmixing

Spectral mixtures observed in hyperspectral imagery often display nonlinear mixing effects. Since most traditional unmixing techniques are based upon the linear mixing model, they perform poorly in finding the correct endmembers and their abundances in the case of nonlinear spectral mixing. In this paper, we present an unmixing algorithm that is capable of extracting endmembers and determining their abundances in hyperspectral imagery under nonlinear mixing assumptions. The algorithm is based upon simplex volume maximization, and uses shortest-path distances in a nearest-neighbor graph in spectral space, hereby respecting the nontrivial geometry of the data manifold in the case of nonlinearly mixed pixels. We demonstrate the algorithm on an artificial data set, the AVIRIS Cuprite data set, and a hyperspectral image of a heathland area in Belgium.

Non-Linear Spectral Unmixing by Geodesic Simplex Volume Maximization

Unlike multispectral (MSI) and panchromatic (PAN) images, generally the spatial resolution of hyperspectral images (HSI) is limited, due to sensor limitations. In many applications, HSI with a high spectral as well as spatial resolution are required. In this paper, a new method for spatial resolution enhancement of a HSI using spectral unmixing and sparse coding (SUSC) is introduced. The proposed method fuses high spectral resolution features from the HSI with high spatial resolution features from an MSI of the same scene. Endmembers are extracted from the HSI by spectral unmixing, and the exact location of the endmembers is obtained from the MSI. This fusion process by using spectral unmixing is formulated as an ill-posed inverse problem which requires a regularization term in order to convert it into a well-posed inverse problem. As a regularizer, we employ sparse coding (SC), for which a dictionary is constructed using high spatial resolution MSI or PAN images from unrelated scenes. The proposed algorithm is applied to real Hyperion and ROSIS datasets. Compared with other state-of-the-art algorithms based on pansharpening, spectral unmixing, and SC methods, the proposed method is shown to significantly increase the spatial resolution while perserving the spectral content of the HSI.

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Rob Heylen

Papers

A Review of Nonlinear Hyperspectral Unmixing Methods

Fully Constrained Least Squares Spectral Unmixing by Simplex Projection

A Multilinear Mixing Model for Nonlinear Spectral Unmixing

Non-Linear Spectral Unmixing by Geodesic Simplex Volume Maximization

Fusion of Hyperspectral and Multispectral Images Using Spectral Unmixing and Sparse Coding