Alina Zare

Endmember Variability in Hyperspectral Analysis: Addressing Spectral Variability During Spectral Unmixing

Variable illumination and environmental, atmospheric, and temporal conditions cause the measured spectral signature for a material to vary within hyperspectral imagery. By ignoring these variations, errors are introduced and propagated throughout hyperspectral image analysis. To develop accurate spectral unmixing and endmember estimation methods, a number of approaches that account for spectral variability have been developed. This article motivates and provides a review for methods that account for spectral variability during hyperspectral unmixing and endmember estimation and a discussion on topics for future work in this area.

Sparsity Promoting Iterated Constrained Endmember Detection in Hyperspectral Imagery

An extension of the iterated constrained endmember (ICE) algorithm that incorporates sparsity-promoting priors to find the correct number of endmembers is presented. In addition to solving for endmembers and endmember fractional maps, this algorithm attempts to autonomously determine the number of endmembers that are required for a particular scene. The number of endmembers is found by adding a sparsity-promoting term to ICEs objective function.

Multi-Modal Change Detection, Application to the Detection of Flooded Areas: Outcome of the 2009–2010 Data Fusion Contest

The 2009-2010 Data Fusion Contest organized by the Data Fusion Technical Committee of the IEEE Geoscience and Remote Sensing Society was focused on the detection of flooded areas using multi-temporal and multi-modal images. Both high spatial resolution optical and synthetic aperture radar data were provided. The goal was not only to identify the best algorithms (in terms of accuracy), but also to investigate the further improvement derived from decision fusion. This paper presents the four awarded algorithms and the conclusions of the contest, investigating both supervised and unsupervised methods and the use of multi-modal data for flood detection. Interestingly, a simple unsupervised change detection method provided similar accuracy as supervised approaches, and a digital elevation model-based predictive method yielded a comparable projected change detection map without using post-event data.

PCE: Piecewise Convex Endmember Detection

A new hyperspectral endmember detection method that represents endmembers as distributions, autonomously partitions the input data set into several convex regions, and simultaneously determines endmember distributions (EDs) and proportion values for each convex region is presented. Spectral unmixing methods that treat endmembers as distributions or hyperspectral images as piecewise convex data sets have not been previously developed. Piecewise convex endmember (PCE) detection can be viewed in two parts. The first part, the ED detection algorithm, estimates a distribution for each endmember rather than estimating a single spectrum. By using EDs, PCE can incorporate an endmembers inherent spectral variation and the variation due to changing environmental conditions. ED uses a new sparsity-promoting polynomial prior while estimating abundance values. The second part of PCE partitions the input hyperspectral data set into convex regions and estimates EDs and proportions for each of these regions. The number of convex regions is determined autonomously using the Dirichlet process. PCE is effective at handling highly mixed hyperspectral images where all of the pixels in the scene contain mixtures of multiple endmembers. Furthermore, each convex region found by PCE conforms to the convex geometry model for hyperspectral imagery. This model requires that the proportions associated with a pixel be nonnegative and sum to one. Algorithm results on hyperspectral data indicate that PCE produces endmembers that represent the true ground-truth classes of the input data set. The algorithm can also effectively represent endmembers as distributions, thus incorporating an endmembers spectral variability.

Hyperspectral Band Selection and Endmember Detection Using Sparsity Promoting Priors

This letter presents a simultaneous band selection and endmember detection algorithm for hyperspectral imagery. This algorithm is an extension of the sparsity promoting iterated constrained endmember (SPICE) algorithm. The extension adds spectral band weights and a sparsity promoting prior to the SPICE objective function to provide integrated band selection. In addition to solving for endmembers, the number of endmembers, and end- member fractional maps, this algorithm attempts to autonomously perform band selection and to determine the number of spectral bands required for a particular scene. Results are presented on a simulated data set and the AVIRIS Indian Pines data set. Experiments on the simulated data set show the ability to find the correct endmembers and abundance values. Experiments on the Indian Pines data set show strong classification accuracies in comparison to previously published results.

Sampling Piecewise Convex Unmixing and Endmember Extraction

A Metropolis-within-Gibbs sampler for piecewise convex hyperspectral unmixing and endmember extraction is presented. The standard linear mixing model used for hyperspectral unmixing assumes that hyperspectral data reside in a single convex region. However, hyperspectral data are often nonconvex. Furthermore, in standard endmember extraction and unmixing methods, endmembers are generally represented as a single point in the high-dimensional space. However, the spectral signature for a material varies as a function of the inherent variability of the material and environmental conditions. Therefore, it is more appropriate to represent each endmember as a full distribution and use this information during spectral unmixing. The proposed method searches for several sets of endmember distributions. By using several sets of endmember distributions, a piecewise convex mixing model is applied, and given this model, the proposed method performs spectral unmixing and endmember estimation given this nonlinear representation of the data. Each set represents a random simplex. The vertices of the random simplex are modeled by the endmember distributions. The hyperspectral data are partitioned into sets associated with each of the extracted sets of endmember distributions using a Dirichlet process prior. The Dirichlet process prior also estimates the number of sets. Thus, the Metropolis-within-Gibbs sampler partitions the data into convex regions, estimates the required number of convex regions, and estimates endmember distributions and abundance values for all convex regions. Results are presented on real hyperspectral and simulated data that indicate the ability of the method to effectively estimate endmember distributions and the number of sets of endmember distributions.

Vegetation Mapping for Landmine Detection Using Long-Wave Hyperspectral Imagery

We develop a vegetation mapping method using long-wave hyperspectral imagery and apply it to landmine detection. The novel aspect of the method is that it makes use of emissivity skewness. The main purpose of vegetation detection for mine detection is to minimize false alarms. Vegetation, such as round bushes, may be mistaken as mines by mine detection algorithms, particularly in synthetic aperture radar (SAR) imagery. We employ an unsupervised vegetation detection algorithm that exploits statistics of emissivity spectra of vegetation in the long-wave infrared spectrum for identification. This information is incorporated into a Choquet integral-based fusion structure, which fuses detector outputs from hyperspectral imagery and SAR imagery. Vegetation mapping is shown to improve mine detection results over a variety of images and fusion models.

Spatial and Spectral Unmixing Using the Beta Compositional Model

This paper introduces the beta compositional model (BCM) for hyperspectral unmixing and four algorithms for unmixing given the BCM. Hyperspectral unmixing estimates the proportion of each endmember at every pixel of a hyperspectral image. Under the BCM, each endmember is a random variable distributed according to a beta distribution. By using a beta distribution, spectral variability is accounted for during unmixing, the reflectance values of each endmember are constrained to a physically realistic range, and skew can be accounted for in the distribution. Spectral variability is incorporated to increase hyperspectral unmixing accuracy. Two BCM-based spectral unmixing approaches are presented: BCM-spectral and BCM-spatial. For each approach, two algorithms, one based on quadratic programming (QP) and one using a Metropolis-Hastings (MH) sampler, are developed. Results indicate that the proposed BCM unmixing algorithms are able to successfully perform unmixing on simulated data and real hyperspectral imagery while incorporating endmember spectral variability and spatial information.

Piecewise Convex Multiple-Model Endmember Detection and Spectral Unmixing

A hyperspectral endmember detection and spectral unmixing algorithm that finds multiple sets of endmembers is presented. Hyperspectral data are often nonconvex. The Piecewise Convex Multiple-Model Endmember Detection algorithm accounts for this using a piecewise convex model. Multiple sets of endmembers and abundances are found using an iterative fuzzy clustering and spectral unmixing method. The results indicate that the piecewise convex representation estimates endmembers that better represent hyperspectral imagery composed of multiple regions where each region is represented with a distinct set of endmembers.

Using physics-based macroscopic and microscopic mixture models for hyperspectral pixel unmixing

A method of incorporating macroscopic and microscopic reflectance models into hyperspectral pixel unmixing is presented and discussed. A vast majority of hyperspectral unmixing methods rely on the linear mixture model to describe pixel spectra resulting from mixtures of endmembers. Methods exist to unmix hyperspectral pixels using nonlinear models, but rely on severely limiting assumptions or estimations of the nonlinearity. This paper will present a hyperspectral pixel unmixing method that utilizes the bidirectional reflectance distribution function to model microscopic mixtures. Using this model, along with the linear mixture model to incorporate macroscopic mixtures, this method is able to accurately unmix hyperspectral images composed of both macroscopic and microscopic mixtures. The mixtures are estimated directly from the hyperspectral data without the need for a priori knowledge of the mixture types. Results are presented using synthetic datasets, of macroscopic and microscopic mixtures, to demonstrate the increased accuracy in unmixing using this new physics-based method over linear methods. In addition, results are presented using a well-known laboratory dataset. Using these results, and other published results from this dataset, increased accuracy in unmixing over other nonlinear methods is shown.