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

Nonlinear unmixing of hyperspectral images using a semiparametric model and spatial regularization

Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an $\ell_1$ local variation norm as the spatial regularizer, is derived. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.Comment: 5 pages, 1 figure, submitted to ICASSP 201

Spectral Target Detecting Using Schroedinger Eigenmaps

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the \potential constraints to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems

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

Generation, validation, and application of abundance map reference data for spectral unmixing

Reference data ( ground truth ) maps traditionally have been used to assess the accuracy of imaging spectrometer classification algorithms. However, these reference data can be prohibitively expensive to produce, often do not include sub-pixel abundance estimates necessary to assess spectral unmixing algorithms, and lack published validation reports. Our research proposes methodologies to efficiently generate, validate, and apply abundance map reference data (AMRD) to airborne remote sensing scenes. We generated scene-wide AMRD for three different remote sensing scenes using our remotely sensed reference data (RSRD) technique, which spatially aggregates unmixing results from fine scale imagery (e.g., 1-m Ground Sample Distance (GSD)) to co-located coarse scale imagery (e.g., 10-m GSD or larger). We validated the accuracy of this methodology by estimating AMRD in 51 randomly-selected 10 m x 10 m plots, using seven independent methods and observers, including field surveys by two observers, imagery analysis by two observers, and RSRD using three algorithms. Results indicated statistically-significant differences between all versions of AMRD, suggesting that all forms of reference data need to be validated. Given these significant differences between the independent versions of AMRD, we proposed that the mean of all (MOA) versions of reference data for each plot and class were most likely to represent true abundances. We then compared each version of AMRD to MOA. Best case accuracy was achieved by a version of imagery analysis, which had a mean coverage area error of 2.0%, with a standard deviation of 5.6%. One of the RSRD algorithms was nearly as accurate, achieving a mean error of 3.0%, with a standard deviation of 6.3%, showing the potential of RSRD-based AMRD generation. Application of validated AMRD to specific coarse scale imagery involved three main parts: 1) spatial alignment of coarse and fine scale imagery, 2) aggregation of fine scale abundances to produce coarse scale imagery-specific AMRD, and 3) demonstration of comparisons between coarse scale unmixing abundances and AMRD. Spatial alignment was performed using our scene-wide spectral comparison (SWSC) algorithm, which aligned imagery with accuracy approaching the distance of a single fine scale pixel. We compared simple rectangular aggregation to coarse sensor point spread function (PSF) aggregation, and found that the PSF approach returned lower error, but that rectangular aggregation more accurately estimated true abundances at ground level. We demonstrated various metrics for comparing unmixing results to AMRD, including mean absolute error (MAE) and linear regression (LR). We additionally introduced reference data mean adjusted MAE (MA-MAE), and reference data confidence interval adjusted MAE (CIA-MAE), which account for known error in the reference data itself. MA-MAE analysis indicated that fully constrained linear unmixing of coarse scale imagery across all three scenes returned an error of 10.83% per class and pixel, with regression analysis yielding a slope = 0.85, intercept = 0.04, and R^2 = 0.81. Our reference data research has demonstrated a viable methodology to efficiently generate, validate, and apply AMRD to specific examples of airborne remote sensing imagery, thereby enabling direct quantitative assessment of spectral unmixing performance

Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems

Nonlinear spectral unmixing of hyperspectral images using Gaussian processes

This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method consists of the Bayesian estimation of the abundance vectors for all the image pixels and the nonlinear function relating the abundance vectors to the observations. The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is evaluated with simulations conducted on synthetic and real data

Multi-scalar remote sensing of the northern mixed prairie vegetation

Optimal scale of study and scaling are fundamental to ecological research, and have been made easier with remotely sensed (RS) data. With access to RS data at multiple scales, it is important to identify how they compare and how effectively information at a specific scale will potentially transfer between scales. Therefore, my research compared the spatial, spectral, and temporal aspects of scale of RS data to study biophysical properties and spatio-temporal dynamics of the northern mixed prairie vegetation. I collected ground cover, dominant species, aboveground biomass, and leaf area index (LAI) from 41 sites and along 3 transects in the West Block of Grasslands National Park of Canada (GNPC; +49°, -107°) between June-July of 2006 and 2007. Narrowband (VIn) and broadband vegetation indices (VIb) were derived from RS data at multiple scales acquired through field spectroradiometry (1 m) and satellite imagery (10, 20, 30 m). VIs were upscaled from their native scales to coarser scales for spatial comparison, and time-series imagery at ~5-year intervals was used for temporal comparison. Results showed VIn, VIb, and LAI captured the spatial variation of plant biophysical properties along topographical gradients and their spatial scales ranged from 35-200 m. Among the scales compared, RS data at finer scales showed stronger ability than coarser scales to estimate ground vegetation. VIn were found to be better predictors than VIb in estimating LAI. Upscaling at all spatial scales showed similar weakening trends for LAI prediction using VIb, however spatial regression methods were necessary to minimize spatial effects in the RS data sets and to improve the prediction results. Multiple endmember spectral mixture analysis (MESMA) successfully captured the spatial heterogeneity of vegetation and effective modeling of sub-pixel spectral variability to produce improved vegetation maps. However, the efficiency of spectral unmixing was found to be highly dependent on the identification of optimal type and number of region-specific endmembers, and comparison of spectral unmixing on imagery at different scales showed spectral resolution to be important over spatial resolution. With the development of a comprehensive endmember library, MESMA may be used as a standard tool for identifying spatio-temporal changes in time-series imagery. Climatic variables were found to affect the success of unmixing, with lower success for years of climatic extremes. Change-detection analysis showed the success of biodiversity conservation practices of GNPC since establishment of the park and suggests that its management strategies are effective in maintaining vegetation heterogeneity in the region. Overall, my research has advanced the understanding of RS of the northern mixed prairie vegetation, especially in the context of effects of scale and scaling. From an eco-management perspective, this research has provided cost- and time-effective methods for vegetation mapping and monitoring. Data and techniques tested in this study will be even more useful with hyperspectral imagery should they become available for the northern mixed prairie