1,145 research outputs found

    Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

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    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

    Diffusion maps for changing data

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    Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications.Comment: 38 pages. 9 figures. To appear in Applied and Computational Harmonic Analysis. v2: Several minor changes beyond just typos. v3: Minor typo corrected, added DO

    Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

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    Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihoodbased classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrencebased texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms

    Manifold learning based spectral unmixing of hyperspectral remote sensing data

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    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

    Algorithms for feature selection and pattern recognition on Grassmann manifolds

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    Includes bibliographical references.2015 Summer.This dissertation presents three distinct application-driven research projects united by ideas and topics from geometric data analysis, optimization, computational topology, and machine learning. We first consider hyperspectral band selection problem solved by using sparse support vector machines (SSVMs). A supervised embedded approach is proposed using the property of SSVMs to exhibit a model structure that includes a clearly identifiable gap between zero and non-zero feature vector weights that permits important bands to be definitively selected in conjunction with the classification problem. An SSVM is trained using bootstrap aggregating to obtain a sample of SSVM models to reduce variability in the band selection process. This preliminary sample approach for band selection is followed by a secondary band selection which involves retraining the SSVM to further reduce the set of bands retained. We propose and compare three adaptations of the SSVM band selection algorithm for the multiclass problem. We illustrate the performance of these methods on two benchmark hyperspectral data sets. Second, we propose an approach for capturing the signal variability in data using the framework of the Grassmann manifold (Grassmannian). Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The resulting points have representations as orthonormal matrices and as such do not reside in Euclidean space in the usual sense. There are a variety of metrics which allow us to determine distance matrices that can be used to realize the Grassmannian as an embedding in Euclidean space. Multidimensional scaling (MDS) determines a low dimensional Euclidean embedding of the manifold, preserving or approximating the Grassmannian geometry based on the distance measure. We illustrate that we can achieve an isometric embedding of the Grassmann manifold using the chordal metric while this is not the case with other distances. However, non-isometric embeddings generated by using the smallest principal angle pseudometric on the Grassmannian lead to the best classification results: we observe that as the dimension of the Grassmannian grows, the accuracy of the classification grows to 100% in binary classification experiments. To build a classification model, we use SSVMs to perform simultaneous dimension selection. The resulting classifier selects a subset of dimensions of the embedding without loss in classification performance. Lastly, we present an application of persistent homology to the detection of chemical plumes in hyperspectral movies. The pixels of the raw hyperspectral data cubes are mapped to the geometric framework of the Grassmann manifold where they are analyzed, contrasting our approach with the more standard framework in Euclidean space. An advantage of this approach is that it allows the time slices in a hyperspectral movie to be collapsed to a sequence of points in such a way that some of the key structure within and between the slices is encoded by the points on the Grassmannian. This motivates the search for topological structure, associated with the evolution of the frames of a hyperspectral movie, within the corresponding points on the manifold. The proposed framework affords the processing of large data sets, such as the hyperspectral movies explored in this investigation, while retaining valuable discriminative information. For a particular choice of a distance metric on the Grassmannian, it is possible to generate topological signals that capture changes in the scene after a chemical release

    Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods

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    Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and the small number of labeled examples typically available for learning. These peculiarities lead to particular signal processing problems, mainly characterized by indetermination and complex manifolds. The framework of statistical learning has gained popularity in the last decade. New methods have been presented to account for the spatial homogeneity of images, to include user's interaction via active learning, to take advantage of the manifold structure with semisupervised learning, to extract and encode invariances, or to adapt classifiers and image representations to unseen yet similar scenes. This tutuorial reviews the main advances for hyperspectral remote sensing image classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201

    Schroedinger Eigenmaps for Manifold Alignment of Multimodal Hyperspectral Images

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    Multimodal remote sensing is an upcoming field as it allows for many views of the same region of interest. Domain adaption attempts to fuse these multimodal remotely sensed images by utilizing the concept of transfer learning to understand data from different sources to learn a fused outcome. Semisupervised Manifold Alignment (SSMA) maps multiple Hyperspectral images (HSIs) from high dimensional source spaces to a low dimensional latent space where similar elements reside closely together. SSMA preserves the original geometric structure of respective HSIs whilst pulling similar data points together and pushing dissimilar data points apart. The SSMA algorithm is comprised of a geometric component, a similarity component and dissimilarity component. The geometric component of the SSMA method has roots in the original Laplacian Eigenmaps (LE) dimension reduction algorithm and the projection functions have roots in the original Locality Preserving Projections (LPP) dimensionality reduction framework. The similarity and dissimilarity component is a semisupervised component that allows expert labeled information to improve the image fusion process. Spatial-Spectral Schroedinger Eigenmaps (SSSE) was designed as a semisupervised enhancement to the LE algorithm by augmenting the Laplacian matrix with a user-defined potential function. However, the user-defined enhancement has yet to be explored in the LPP framework. The first part of this thesis proposes to use the Spatial-Spectral potential within the LPP algorithm, creating a new algorithm we call the Schroedinger Eigenmap Projections (SEP). Through experiments on publicly available data with expert-labeled ground truth, we perform experiments to compare the performance of the SEP algorithm with respect to the LPP algorithm. The second part of this thesis proposes incorporating the Spatial Spectral potential from SSSE into the SSMA framework. Using two multi-angled HSI’s, we explore the impact of incorporating this potential into SSMA

    Feature extraction and fusion for classification of remote sensing imagery

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