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

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

A geometric approach to archetypal analysis and non-negative matrix factorization

Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by interpreting both problems as finding extreme points of the data cloud. We also develop and analyze an efficient approach to finding extreme points in high dimensions. For modern massive datasets that are too large to fit on a single machine and must be stored in a distributed setting, our approach makes only a small number of passes over the data. In fact, it is possible to obtain the NMF or perform archetypal analysis with just two passes over the data.Comment: 36 pages, 13 figure

Hyperspectral Unmixing Based on Dual-Depth Sparse Probabilistic Latent Semantic Analysis

This paper presents a novel approach for spectral unmixing of remotely sensed hyperspectral data. It exploits probabilistic latent topics in order to take advantage of the semantics pervading the latent topic space when identifying spectral signatures and estimating fractional abundances from hyperspectral images. Despite the contrasted potential of topic models to uncover image semantics, they have been merely used in hyperspectral unmixing as a straightforward data decomposition process. This limits their actual capabilities to provide semantic representations of the spectral data. The proposed model, called dual-depth sparse probabilistic latent semantic analysis (DEpLSA), makes use of two different levels of topics to exploit the semantic patterns extracted from the initial spectral space in order to relieve the ill-posed nature of the unmixing problem. In other words, DEpLSA defines a first level of deep topics to capture the semantic representations of the spectra, and a second level of restricted topics to estimate endmembers and abundances over this semantic space. An experimental comparison in conducted using the two standard topic models and the seven state-of-the-art unmixing methods available in the literature. Our experiments, conducted using four different hyperspectral images, reveal that the proposed approach is able to provide competitive advantages over available unmixing approaches

Linear Unmixing of Hyperspectral Signals via Wavelet Feature Extraction

A pixel in remotely sensed hyperspectral imagery is typically a mixture of multiple electromagnetic radiances from various ground cover materials. Spectral unmixing is a quantitative analysis procedure used to recognize constituent ground cover materials (or endmembers) and obtain their mixing proportions (or abundances) from a mixed pixel. The abundances are typically estimated using the least squares estimation (LSE) method based on the linear mixture model (LMM). This dissertation provides a complete investigation on how the use of appropriate features can improve the LSE of endmember abundances using remotely sensed hyperspectral signals. The dissertation shows how features based on signal classification approaches, such as discrete wavelet transform (DWT), outperform features based on conventional signal representation methods for dimensionality reduction, such as principal component analysis (PCA), for the LSE of endmember abundances. Both experimental and theoretical analyses are reported in the dissertation. A DWT-based linear unmixing system is designed specially for the abundance estimation. The system utilizes the DWT as a pre-processing step for the feature extraction. Based on DWT-based features, the system utilizes the constrained LSE for the abundance estimation. Experimental results show that the use of DWT-based features reduces the abundance estimation deviation by 30-50% on average, as compared to the use of original hyperspectral signals or conventional PCA-based features. Based on the LMM and the LSE method, a series of theoretical analyses are derived to reveal the fundamental reasons why the use of the appropriate features, such as DWT-based features, can improve the LSE of endmember abundances. Under reasonable assumptions, the dissertation derives a generalized mathematical relationship between the abundance estimation error and the endmember separabilty. It is proven that the abundance estimation error can be reduced through increasing the endmember separability. The use of DWT-based features provides a potential to increase the endmember separability, and consequently improves the LSE of endmember abundances. The stability of the LSE of endmember abundances is also analyzed using the concept of the condition number. Analysis results show that the use of DWT-based features not only improves the LSE of endmember abundances, but also improves the LSE stability

Canonical Correlation Feature Selection for Sensors with Overlapping Bands: Theory and Application

The main focus of this paper is a rigorous development and validation of a novel canonical correlation feature- selection (CCFS) algorithm that is particularly well suited for spectral sensors with overlapping and noisy bands. The proposed approach combines a generalized canonical correlation analysis framework and a minimum mean-square-error criterion for the selection of feature subspaces. The latter induces ranking of the best linear combinations of the noisy overlapping bands and, in doing so, guarantees a minimal generalized distance between the centers of classes and their respective reconstructions in the space spanned by sensor bands. To demonstrate the efficacy and the scope of the proposed approach, two different applications are considered. The first one is separability and classification analysis of rock species using laboratory spectral data and a quantum-dot infrared photodetector (QDIP) sensor. The second application deals with supervised classification and spectral unmixing, and abundance estimation of hyperspectral imagery obtained from the Airborne Hyperspectral Imager sensor. Since QDIP bands exhibit significant spectral overlap, the first study validates the new algorithm in this important application context. The results demonstrate that proper postprocessing can facilitate the emergence of QDIP-based sensors as a promising technology for midwave- and longwave-infrared remote sensing and spectral imaging. In particular, the proposed CCFS algorithm makes it possible to exploit the unique advantage offered by QDIPs with a dot-in-a-well configuration, comprising their bias-dependent spectral response, which is attributable to the quantum Stark effect. The main objective of the second study is to assert that the scope of the new CCFS approach also extends to more traditional spectral sensors

SULoRA: Subspace Unmixing with Low-Rank Attribute Embedding for Hyperspectral Data Analysis

To support high-level analysis of spaceborne imaging spectroscopy (hyperspectral) imagery, spectral unmixing has been gaining significance in recent years. However, from the inevitable spectral variability, caused by illumination and topography change, atmospheric effects and so on, makes it difficult to accurately estimate abundance maps in spectral unmixing. Classical unmixing methods, e.g. linear mixing model (LMM), extended linear mixing model (ELMM), fail to robustly handle this issue, particularly facing complex spectral variability. To this end, we propose a subspace-based unmixing model using low-rank learning strategy, called subspace unmixing with low-rank attribute embedding (SULoRA), robustly against spectral variability in inverse problems of hyperspectral unmixing. Unlike those previous approaches that unmix the spectral signatures directly in original space, SULoRA is a general subspace unmixing framework that jointly estimates subspace projections and abundance maps in order to find a ‘raw’ subspace which is more suitable for carrying out the unmixing procedure. More importantly, we model such ‘raw’ subspace with low-rank attribute embedding. By projecting the original data into a low-rank subspace, SULoRA can effectively address various spectral variabilities in spectral unmixing. Furthermore, we adopt an alternating direction method of multipliers (ADMM) based to solve the resulting optimization problem. Extensive experiments on synthetic and real datasets are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods