Paul D. Gader

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 Mustards unmixing tutorial 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.

Landmine detection with ground penetrating radar using hidden Markov models

Novel, general methods for detecting landmine signatures in ground penetrating radar (GPR) using hidden Markov models (HMMs) are proposed and evaluated. The methods are evaluated on real data collected by a GPR mounted on a moving vehicle at three different geographical locations. A large library of digital GPR signatures of both landmines and clutter/background was constructed and used for training. Simple, but effective, observation vector representations are constructed to naturally model the time-varying signatures produced by the interaction of the GPR and the landmines as the vehicle moves. The number and definition of the states of the HMMs are based on qualitative signature models. The model parameters are optimized using the Baum-Welch algorithm. The models were trained on landmine and background/clutter signatures from one geographical location and successfully tested at two different locations. The data used in the test were acquired from over 6000 m/sup 2/ of simulated dirt and gravel roads, and also off-road conditions. These data contained approximately 300 landmine signatures, over half of which were plastic-cased or completely nonmetal.

Image algebra techniques for parallel image processing

We present a new model of parallel computation—the LogGP model—and use it to analyze a number of algorithms, most notably, the single node scatter (one-to-all personalized broadcast). The LogGP model is an extension of the LogP model for parallel computation which abstracts the communication of fixed-sized short messages through the use of four parameters: the communication latency (L), overhead (o), bandwidth ( g), and the number of processors ( P). As evidenced by experimental data, the LogP model can accurately predict communication performance when only short messages are sent (as on the CM-5). However, many existing parallel machines have special support for long messages and achieve a much higher bandwidth for long messages than for short messages (e.g., IBM SP-2, Paragon, Meiko CS-2, Ncube/ 2). We extend the basic LogP model with a linear model for long messages. This combination, which we call the LogGP model of parallel computation, has one additional parameter,G, which captures the bandwidth obtained for long messages. Experimental data collected on the Meiko CS-2 shows that this simple extension of the LogP model can quite accurately predict communication performance for both short and long messages. This paper discusses algorithm design and analysis under the new model. We also examine, in more detail, the single node scatter problem under LogGP. We derive solutions for this problem which are qualitatively different from those obtained under the simpler LogP model, reflecting the importance of capturing long messages in a model.

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing (SP) for hyperspectral remote sensing [1], [2]. Blind HU aims at identifying materials present in a captured scene, as well as their compositions, by using high spectral resolution of hyperspectral images. It is a blind source separation (BSS) problem from a SP viewpoint. Research on this topic started in the 1990s in geoscience and remote sensing [3]-[7], enabled by technological advances in hyperspectral sensing at the time. In recent years, blind HU has attracted much interest from other fields such as SP, machine learning, and optimization, and the subsequent cross-disciplinary research activities have made blind HU a vibrant topic. The resulting impact is not just on remote sensing - blind HU has provided a unique problem scenario that inspired researchers from different fields to devise novel blind SP methods. In fact, one may say that blind HU has established a new branch of BSS approaches not seen in classical BSS studies. In particular, the convex geometry concepts - discovered by early remote sensing researchers through empirical observations [3]-[7] and refined by later research - are elegant and very different from statistical independence-based BSS approaches established in the SP field. Moreover, the latest research on blind HU is rapidly adopting advanced techniques, such as those in sparse SP and optimization. The present development of blind HU seems to be converging to a point where the lines between remote sensing-originated ideas and advanced SP and optimization concepts are no longer clear, and insights from both sides would be used to establish better methods.

Handwritten word recognition using segmentation-free hidden Markov modeling and segmentation-based dynamic programming techniques

A lexicon-based, handwritten word recognition system combining segmentation-free and segmentation-based techniques is described. The segmentation-free technique constructs a continuous density hidden Markov model for each lexicon string. The segmentation-based technique uses dynamic programming to match word images and strings. The combination module uses differences in classifier capabilities to achieve significantly better performance.

Fusion of handwritten word classifiers

Methods for fusing multiple handwritten word classifiers are compared on standard data. A novel method based on data-dependent densities in a Choquet fuzzy integral is shown to outperform neural networks, Borda and weighted Borda counts, and Sugeno fuzzy integral.

Advances in fuzzy integration for pattern recognition

Abstract Uncertainty abounds in pattern recognition problems. Therefore, management of uncertainty is an important problem in the development of automated systems for the detection, recognition, and interpretation of objects from their feature measurements. Fuzzy set theory offers numerous methodologies for the modeling and management of uncertainty. One such fuzzy set theoretic technology which has proven quite useful in pattern recognition is the fuzzy integral. The purpose of this paper is to examine new utilizations of the fuzzy integral as a decision making model in the area of object recognition. In particular, we develop generalizations of the fuzzy integral and show that these generalizations can achieve higher recognition rates in an automatic target recognition problem. Also, we demonstrate significant increases in recognition rates using the fuzzy integral to fuse the results of different neural network classifiers in a complex handwritten character recognition domain.

Handwritten word recognition with character and inter-character neural networks

An off-line handwritten word recognition system is described. Images of handwritten words are matched to lexicons of candidate strings. A word image is segmented into primitives. The best match between sequences of unions of primitives and a lexicon string is found using dynamic programming. Neural networks assign match scores between characters and segments. Two particularly unique features are that neural networks assign confidence that pairs of segments are compatible with character confidence assignments and that this confidence is integrated into the dynamic programming. Experimental results are provided on data from the U.S. Postal Service.

A Review of Nonlinear Hyperspectral Unmixing Methods

In hyperspectral unmixing, the prevalent model used is the linear mixing model, and a large variety of techniques based on this model has been proposed to obtain endmembers and their abundances in hyperspectral imagery. However, it has been known for some time that nonlinear spectral mixing effects can be a crucial component in many real-world scenarios, such as planetary remote sensing, intimate mineral mixtures, vegetation canopies, or urban scenes. While several nonlinear mixing models have been proposed decades ago, only recently there has been a proliferation of nonlinear unmixing models and techniques in the signal processing literature. This paper aims to give an historical overview of the majority of nonlinear mixing models and nonlinear unmixing methods, and to explain some of the more popular techniques in detail. The main models and techniques treated are bilinear models, models for intimate mineral mixtures, radiosity-based approaches, ray tracing, neural networks, kernel methods, support vector machine techniques, manifold learning methods, piece-wise linear techniques, and detection methods for nonlinearity. Furthermore, we provide an overview of several recent developments in the nonlinear unmixing literature that do not belong into any of these categories.

Detection and Discrimination of Land Mines in Ground-Penetrating Radar Based on Edge Histogram Descriptors and a Possibilistic

This paper describes an algorithm for land mine detection using sensor data generated by a ground-penetrating radar (GPR) system that uses edge histogram descriptors for feature extraction and a possibilistic K -nearest neighbors (K-NNs) rule for confidence assignment. The algorithm demonstrated the best performance among several high-performance algorithms in extensive testing on a large real-world datasets associated with the difficult problem of land mine detection. The superior performance of the algorithm is attributed to the use of the possibilistic K -NN algorithm, thereby providing important evidence supporting the use of possibilistic methods in real-world applications. The GPR produces a 3-D array of intensity values, representing a volume below the surface of the ground. First, a computationally inexpensive prescreening algorithm for anomaly detection is used to focus attention and identify candidate signatures that resemble mines. The identified regions of interest are processed further by a feature extraction algorithm to capture their salient features. We use translation-invariant features that are based on the local edge distribution of the 3-D GPR signatures. Specifically, each 3-D signature is divided into subsignatures, and the local edge distribution for each subsignature is represented by a histogram. Next, the training signatures are clustered to identify prototypes. The main idea is to identify few prototypes that can capture the variations of the signatures within each class. These variations could be due to different mine types, different soil conditions, different weather conditions, etc. Fuzzy memberships are assigned to these representatives to capture their degree of sharing among the mines and false alarm classes. Finally, a possibilistic K-NN-based rule is used to assign a confidence value to distinguish true detections from false alarms. The proposed algorithm is implemented and integrated within a complete land mine prototype system. It is trained, field-tested, evaluated, and compared using a large-scale cross-validation experiment that uses a diverse dataset acquired from four outdoor test sites at different geographic locations. This collection covers over 41 807 m2 of ground and includes 1593 mine encounters.