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

Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are verified by numerical simulations

Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

International audienceMixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images

Context dependent spectral unmixing.

A hyperspectral unmixing algorithm that finds multiple sets of endmembers is proposed. The algorithm, called Context Dependent Spectral Unmixing (CDSU), is a local approach that adapts the unmixing to different regions of the spectral space. It is based on a novel function that combines context identification and unmixing. This joint objective function models contexts as compact clusters and uses the linear mixing model as the basis for unmixing. Several variations of the CDSU, that provide additional desirable features, are also proposed. First, the Context Dependent Spectral unmixing using the Mahalanobis Distance (CDSUM) offers the advantage of identifying non-spherical clusters in the high dimensional spectral space. Second, the Cluster and Proportion Constrained Multi-Model Unmixing (CC-MMU and PC-MMU) algorithms use partial supervision information, in the form of cluster or proportion constraints, to guide the search process and narrow the space of possible solutions. The supervision information could be provided by an expert, generated by analyzing the consensus of multiple unmixing algorithms, or extracted from co-located data from a different sensor. Third, the Robust Context Dependent Spectral Unmixing (RCDSU) introduces possibilistic memberships into the objective function to reduce the effect of noise and outliers in the data. Finally, the Unsupervised Robust Context Dependent Spectral Unmixing (U-RCDSU) algorithm learns the optimal number of contexts in an unsupervised way. The performance of each algorithm is evaluated using synthetic and real data. We show that the proposed methods can identify meaningful and coherent contexts, and appropriate endmembers within each context. The second main contribution of this thesis is consensus unmixing. This approach exploits the diversity and similarity of the large number of existing unmixing algorithms to identify an accurate and consistent set of endmembers in the data. We run multiple unmixing algorithms using different parameters, and combine the resulting unmixing ensemble using consensus analysis. The extracted endmembers will be the ones that have a consensus among the multiple runs. The third main contribution consists of developing subpixel target detectors that rely on the proposed CDSU algorithms to adapt target detection algorithms to different contexts. A local detection statistic is computed for each context and then all scores are combined to yield a final detection score. The context dependent unmixing provides a better background description and limits target leakage, which are two essential properties for target detection algorithms

Blind source Separation for MT-InSAR analysis with structural health monitoring applications

Monitoring large areas of the Earth's surface is possible thanks to the availability of remote sensing data obtained by a large collection of diverse satellites orbiting the Earth. Specifically, multitemporal interferometric synthetic aperture radar (MT-InSAR) techniques supply the structural community with time series of line-of-sight displacements of terrain or structures, such as bridges or buildings, resulting from causes such as thermal expansion, contraction, and terrain deformation. The analysis of the different deformation signals observed is crucial in order to identify the different phenomena that cause the deformation. In this article, we explore the possibility of applying blind source separation algorithms to MT-InSAR, with the aim of developing methods towards automatic identification of different deformation patterns both in buildings and structures. We validate the proposed methodology using both synthetically generated datasets and real MT-InSAR data. We also provide a comparison with other similar methods. Our results demonstrate that InSAR time-series analysis can benefit from the use of the proposed blind source separation approach. Furthermore, the proposed technique is robust to the noise which is usually present in MT-InSAR data. This opens the door for monitoring infrastructure at scale over very large areas, helping to monitor civil infrastructures, and providing relevant insights to asset owners regarding the performance of such structures over time