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

Discriminant Analysis with Spatial Weights for Urban Land Cover Classification

Classifying urban area images is challenging because of the heterogeneous nature of the urban landscape resulting in mixed pixels and classes with highly variable spectral ranges. Approaches using ancillary data, such as knowledge based or expert systems, have shown to improve the classification accuracy in urban areas. Appropriate ancillary data, however, may not always be available. The goal of this study is to compare the results of the discriminant analysis statistical technique with discriminant analysis with spatial weights to classify urban land cover. Discriminant analysis is a statistical technique used to predict group membership for a target based on the linear combination of independent variables. Strict per pixel statistical analysis however does not consider the spatial dependencies among neighbouring pixels. Our study shows that approaches using ancillary data continue to outperform strict spectral classifiers but that using a spatial weight improved the results. Furthermore, results show that when the discriminant analysis technique works well then the spatially weighted approach performs better. However, when the discriminant analysis performs poorly, those poor results are magnified in the spatially weighted approach in the same study area. The study shows that for dominant classes, adding spatial weights improves the classification accuracy.

Uncertainty Assessment of Spectral Mixture Analysis in Remote Sensing Imagery

Spectral mixture analysis (SMA), a scheme of sub-pixel-based classifications, is one of the widely used models to map fractional land use and land cover information in remote sensing imagery. It assumes that: 1) a mixed pixel is composed by several pure land cover classes (endmembers) linearly or nonlinearly, and 2) the spectral signature of each endmember is a constant within the entire spatial extent of analysis. SMA has been commonly applied to impervious surface area extraction, vegetation fraction estimation, and land use and land cover change (LULC) mapping. Limitations of SMA, however, still exist. First, the existence of between- and within-class variability prevents the selection of accurate endmembers, which results in poor accuracy of fractional land cover estimates. Weighted spectral mixture analysis (WSMA) and transformed spectral mixture analysis (TSMA) are alternate means to address the within- and between- class variability. These methods, however, have not been analyzed systematically and comprehensively. The effectiveness of each WSMA and TSMA scheme is still unknown, in particular within different urban areas. Second, multiple endmember SMA (MESMA) is a better alternative to address spectral mixture model uncertainties. It, nonetheless, is time consuming and inefficient. Further, incorrect endmember selections may still limit model performance as the best-fit endmember model might not be the optimal model due to the existence of spectral variability. Therefore, this study aims 1) to explore endmember uncertainties by examining WSMA and TSMA modeling comprehensively, and 2) to develop an improved MESMA model in order to address the uncertainties of spectral mixture models. Results of the WSMA examination illustrated that some weighting schemes did reduce endmember uncertainties since they could improve the fractional estimates significantly. The results also indicated that spectral class variance played a key role in addressing the endmember uncertainties, as the better performing weighting schemes were constructed with spectral class variance. In addition, the results of TSMA examination demonstrated that some TSMAs, such as normalized spectral mixture analysis (NSMA), could effectively solve the endmember uncertainties because of their stable performance in different study areas. Results of Class-based MEMSA (C-MESMA) indicated that it could address spectral mixture model uncertainties by reducing a lot of the calculation burden and effectively improving accuracy. Assessment demonstrated that C-MEMSA significantly improving accuracy. Major contributions of this study can be summarized as follow. First, the effectiveness of addressing endmember uncertainties have been fully discussed by examining: 1) the effectiveness of ten weighted spectral mixture models in urban environments; and 2) the effectiveness of 26 transformed spectral mixture models in three locations. Constructive guidance regarding handling endmember uncertainties using WSMA and TSMA have been provided. Second, the uncertainties of spectral mixture model were reduced by developing an improved MESMA model, named C-MESMA. C-MESMA could restrict the distribution of endmembers and reduce the calculation burden of traditional MESMA, increasing SMA accuracy significantly

Manifold learning based spectral unmixing of hyperspectral remote sensing data

Nonlinear mixing effects inherent in hyperspectral data are not properly represented in linear spectral unmixing models. Although direct nonlinear unmixing models provide capability to capture nonlinear phenomena, they are difficult to formulate and the results are not always generalizable. Manifold learning based spectral unmixing accommodates nonlinearity in the data in the feature extraction stage followed by linear mixing, thereby incorporating some characteristics of nonlinearity while retaining advantages of linear unmixing approaches. Since endmember selection is critical to successful spectral unmixing, it is important to select proper endmembers from the manifold space. However, excessive computational burden hinders development of manifolds for large-scale remote sensing datasets. This dissertation addresses issues related to high computational overhead requirements of manifold learning for developing representative manifolds for the spectral unmixing task. Manifold approximations using landmarks are popular for mitigating the computational complexity of manifold learning. A new computationally effective landmark selection method that exploits spatial redundancy in the imagery is proposed. A robust, less costly landmark set with low spectral and spatial redundancy is successfully incorporated with a hybrid manifold which shares properties of both global and local manifolds. While landmark methods reduce computational demand, the resulting manifolds may not represent subtle features of the manifold adequately. Active learning heuristics are introduced to increase the number of landmarks, with the goal of developing more representative manifolds for spectral unmixing. By communicating between the landmark set and the query criteria relative to spectral unmixing, more representative and stable manifolds with less spectrally and spatially redundant landmarks are developed. A new ranking method based on the pixels with locally high spectral variability within image subsets and convex-geometry finds a solution more quickly and precisely. Experiments were conducted to evaluate the proposed methods using the AVIRIS Cuprite hyperspectral reference dataset. A case study of manifold learning based spectral unmixing in agricultural areas is included in the dissertation.Remotely sensed data collected by airborne or spaceborne sensors are utilized to quantify crop residue cover over an extensive area. Although remote sensing indices are popular for characterizing residue amounts, they are not effective with noisy Hyperion data because the effect of residual striping artifacts is amplified in ratios involving band differences. In this case study, spectral unmixing techniques are investigated for estimating crop residue as an alternative approach to empirical models developed using band based indices. The spectral unmixing techniques, and especially the manifold learning approaches, provide more robust, lower RMSE estimates for crop residue cover than the hyperspectral index based method for Hyperion data

Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between physical parameters and spectra has been established in a data-driven fashion, the learned relationship can be used to estimate physical parameters for new hyper-spectral observations. Within this framework, we propose a spatially-constrained and partially-latent regression method which maps high-dimensional inputs (hyper-spectral images) onto low-dimensional responses (physical parameters such as the local chemical composition of the soil). The proposed regression model comprises two key features. Firstly, it combines a Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent response model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. Secondly, spatial constraints are introduced in the model through a Markov random field (MRF) prior which provides a spatial structure to the Gaussian-mixture hidden variables. Experiments conducted on a database composed of remotely sensed observations collected from the Mars planet by the Mars Express orbiter demonstrate the effectiveness of the proposed model.Comment: 12 pages, 4 figures, 3 table

Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package

Spectral pixels are often a mixture of the pure spectra of the materials, called endmembers, due to the low spatial resolution of hyperspectral sensors, double scattering, and intimate mixtures of materials in the scenes. Unmixing estimates the fractional abundances of the endmembers within the pixel. Depending on the prior knowledge of endmembers, linear unmixing can be divided into three main groups: supervised, semi-supervised, and unsupervised (blind) linear unmixing. Advances in Image processing and machine learning substantially affected unmixing. This paper provides an overview of advanced and conventional unmixing approaches. Additionally, we draw a critical comparison between advanced and conventional techniques from the three categories. We compare the performance of the unmixing techniques on three simulated and two real datasets. The experimental results reveal the advantages of different unmixing categories for different unmixing scenarios. Moreover, we provide an open-source Python-based package available at https://github.com/BehnoodRasti/HySUPP to reproduce the results