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

EndNet: Sparse AutoEncoder Network for Endmember Extraction and Hyperspectral Unmixing

Data acquired from multichannel sensors are a highly valuable asset to interpret the environment for a variety of remote sensing applications. However, low spatial resolution is a critical limitation for previous sensors, and the constituent materials of a scene can be mixed in different fractions due to their spatial interactions. Spectral unmixing is a technique that allows us to obtain the material spectral signatures and their fractions from hyperspectral data. In this paper, we propose a novel endmember extraction and hyperspectral unmixing scheme, so-called EndNet, that is based on a two-staged autoencoder network. This well-known structure is completely enhanced and restructured by introducing additional layers and a projection metric [i.e., spectral angle distance (SAD) instead of inner product] to achieve an optimum solution. Moreover, we present a novel loss function that is composed of a Kullback-Leibler divergence term with SAD similarity and additional penalty terms to improve the sparsity of the estimates. These modifications enable us to set the common properties of endmembers, such as nonlinearity and sparsity for autoencoder networks. Finally, due to the stochastic-gradient-based approach, the method is scalable for large-scale data and it can be accelerated on graphical processing units. To demonstrate the superiority of our proposed method, we conduct extensive experiments on several well-known data sets. The results confirm that the proposed method considerably improves the performance compared to the state-of-the-art techniques in the literature

Nonlinear Spectral Unmixing using Semi-Supervised Standard Fuzzy Clustering

Coarse resolution captured in remote sensing causes the combination of different materials in one pixel, called the mixed pixel. Spectral unmixing estimates the combination of endmembers in mixed pixels and their corresponding abundance maps in the Hyper/Multi spectral image. In this paper, a nonlinear spectral unmixing based on semi-supervised fuzzy clustering is proposed. First, pure pixels (endmembers) using Vertex Component Analysis (VCA) are extracted and those pixels are the labelled pixels where the membership value of each is 1 for the corresponding endmember and 0 for the others. Second, the semi-supervised fuzzy clustering is applied to find the membership matrix defining the fraction of the endmember in each mixed pixel and hence extract the abundance maps. The experiments were conducted on both synthetic data such as the Legendre data and real data such as Jasper Ridge data. The non-linearity of the Legendre data was performed by the Fan model on different signal-tonoise ratio values. The results of the new unmixing model show its significant performance when compared with four state-of the art unmixing algorithm

Improvements to algorithms for hyperspectral linear unmixing based on statistical model

Spectral mixing is one of the main problems that arise when characterizing the spectral constituents residing at a sub-pixel level in a hyperspectral scene. In this work we propose a improvement of the algorithms based on statistical model, i.e. NCM, with a novel sampling approach inspired by Genetic Algorithms. Furthermore, linearization is introduced to reduce computational complexity

Automatic Denoising and Unmixing in Hyperspectral Image Processing

This thesis addresses two important aspects in hyperspectral image processing: automatic hyperspectral image denoising and unmixing. The first part of this thesis is devoted to a novel automatic optimized vector bilateral filter denoising algorithm, while the remainder concerns nonnegative matrix factorization with deterministic annealing for unsupervised unmixing in remote sensing hyperspectral images. The need for automatic hyperspectral image processing has been promoted by the development of potent hyperspectral systems, with hundreds of narrow contiguous bands, spanning the visible to the long wave infrared range of the electromagnetic spectrum. Due to the large volume of raw data generated by such sensors, automatic processing in the hyperspectral images processing chain is preferred to minimize human workload and achieve optimal result. Two of the mostly researched processing for such automatic effort are: hyperspectral image denoising, which is an important preprocessing step for almost all remote sensing tasks, and unsupervised unmixing, which decomposes the pixel spectra into a collection of endmember spectral signatures and their corresponding abundance fractions. Two new methodologies are introduced in this thesis to tackle the automatic processing problems described above. Vector bilateral filtering has been shown to provide good tradeoff between noise removal and edge degradation when applied to multispectral/hyperspectral image denoising. It has also been demonstrated to provide dynamic range enhancement of bands that have impaired signal to noise ratios. Typical vector bilateral filtering usage does not employ parameters that have been determined to satisfy optimality criteria. This thesis also introduces an approach for selection of the parameters of a vector bilateral filter through an optimization procedure rather than by ad hoc means. The approach is based on posing the filtering problem as one of nonlinear estimation and minimizing the Stein\u27s unbiased risk estimate (SURE) of this nonlinear estimator. Along the way, this thesis provides a plausibility argument with an analytical example as to why vector bilateral filtering outperforms band-wise 2D bilateral filtering in enhancing SNR. Experimental results show that the optimized vector bilateral filter provides improved denoising performance on multispectral images when compared to several other approaches. Non-negative matrix factorization (NMF) technique and its extensions were developed to find part based, linear representations of non-negative multivariate data. They have been shown to provide more interpretable results with realistic non-negative constrain in unsupervised learning applications such as hyperspectral imagery unmixing, image feature extraction, and data mining. This thesis extends the NMF method by incorporating deterministic annealing optimization procedure, which will help solve the non-convexity problem in NMF and provide a better choice of sparseness constrain. The approach is based on replacing the difficult non-convex optimization problem of NMF with an easier one by adding an auxiliary convex entropy constrain term and solving this first. Experiment results with hyperspectral unmixing application show that the proposed technique provides improved unmixing performance compared to other state-of-the-art methods