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

Hyperspectral Endmember Extraction Techniques

Hyperspectral data processing and analysis mainly plays a vital role in detection, identification, discrimination and estimation of earth surface materials. It involves atmospheric correction, dimensionality reduction, endmember extraction, spectral unmixing and classification phases. One of the ultimate aims of hyperspectral data processing and analysis is to achieve high classification accuracy. The classification accuracy of hyperspectral data most probably depends upon image-derived endmembers. Ideally, an endmember is defined as a spectrally unique, idealized and pure signature of a surface material. Extraction of consistent and desired endmember is one of the important criteria to achieve the high accuracy of hyperspectral data classification and spectral unmixing. Several methods, strategies and algorithms are proposed by various researchers to extract the endmembers from hyperspectral imagery. Most of these techniques and algorithms are significantly dependent on user-defined input parameters, and this issue is subjective because there is no standard specificity about these input parameters. This leads to inconsistencies in overall endmember extraction. To resolve the aforementioned problems, systematic, generic, robust and automated mechanism of endmember extraction is required. This chapter gives and highlights the generic approach of endmember extraction with popular algorithm limitations and challenges

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

Using n-dimensional volumes for mathematical applications in spectral image analysis

The ability to detect an object or activity -- such as a military vehicle, construction area, campsite, or vehicle tracks -- is highly important to both military and civilian applications. Sensors that process multi and hyperspectral images provide a medium for performing such tasks. Hyperspectral imaging is a technique for collecting and processing imagery at a large number of visible and non-visible wavelengths. Different materials exhibit different trends in their spectra, which can be used to analyze the image. For an image collected at n different wavelengths, the spectrum of each pixel can be mathematically represented as an n-element vector. The algorithm established in this work, the Simplex Volume Estimation algorithm (SVE), focuses specifically on change detection and large area search. In hyperspectral image analysis, a set of pixels constitutes a data cloud, with each pixel corresponding to a vector endpoint in Euclidean space. The SVE algorithm takes a geometrical approach to image analysis based on the linear mixture model, which describes each pixel in an image collected at n spectral bands as a linear combination of n+1 pure-material component spectra (known as endmembers). Iterative endmember identification is used to construct a \u27volume function,\u27 where the Gram matrix is used to calculate the hypervolume of the data at each iteration as the endmembers are considered in Euclidean spaces of increasing dimensionality. Linear algebraic theory substantiates that the volume function accurately characterizes the inherent dimensionality of a set of data, and supports that the volume function provides a tool for identifying the subspace in which the magnitude of the spread of the data is the greatest. A metric is extracted from the volume function, and is used to quantify the relative complexity within a single image or the change in complexity across multiple images. The SVE algorithm was applied to hyperspectral images for the tasks of change detection and large area search, and the results from these applications will demonstrate the feasibility of this method as a cueing tool for analysts

Hyperspectral sub-pixel target detection using hybrid algorithms and Physics Based Modeling

This thesis develops a new hybrid target detection algorithm called the Physics Based-Structured InFeasibility Target-detector (PB-SIFT) which incorporates Physics Based Modeling (PBM) along with a new Structured Infeasibility Projector (SIP) metric. Traditional matched filters are susceptible to leakage or false alarms due to bright or saturated pixels that appear target-like to hyperspectral detection algorithms but are not truly target. This detector mitigates against such false alarms. More often than not, detection algorithms are applied to atmospherically compensated hyperspectral imagery. Rather than compensate the imagery, we take the opposite approach by using a physics based model to generate permutations of what the target might look like as seen by the sensor in radiance space. The development and status of such a method is presented as applied to the generation of target spaces. The generated target spaces are designed to fully encompass image target pixels while using a limited number of input model parameters. Evaluation of such target spaces shows that they can reproduce a HYDICE image target pixel spectrum to less than 1% RMS error (equivalent reflectance) in the visible and less than 6% in the near IR. Background spaces are modeled using a linear subspace (structured) approach characterized by basis vectors found by using the maximum distance method (MaxD). The SIP is developed along with a Physics Based Orthogonal Projection Operator (PBosp) which produces a 2 dimensional decision space. Results from the HYDICE FR I data set show that the physics based approach, along with the PB-SIFT algorithm, can out perform the Spectral Angle Mapper (SAM) and Spectral Matched Filter (SMF) on both exposed and fully concealed man-made targets found in hyperspectral imagery. Furthermore, the PB-SIFT algorithm performs as good (if not better) than the Mixture Tuned Matched Filter (MTMF)

An overview on hyperspectral unmixing: Geometrical, statistical, and sparse regression based approaches

Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hun-dreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scan-ner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vec-tors (collection of signals acquired at different spectral bands from a given pixel) acquired by the hyperspectral scanners are actually mixtures of the spectral signatures of the materials present in the scene. Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances. Spectral unmix