Comparison of Basis-Vector Selection Methods for Target and Background Subspaces as Applied to Subpixel Target Detection

This paper focuses on comparing three basis-vector selection techniques as applied to target detection in hyperspectral imagery. The basis-vector selection methods tested were the singular value decomposition (SVD), pixel purity index (PPI), and a newly developed approach called the maximum distance (MaxD) method. Target spaces were created using an illumination invariant technique, while the background space was generated from AVIRIS hyperspectral imagery. All three selection techniques were applied (in various combinations) to target as well as background spaces so as to generate dimensionally-reduced subspaces. Both target and background subspaces were described by linear subspace models (i.e., structured models). Generated basis vectors were then implemented in a generalized likelihood ratio (GLR) detector. False alarm rates (FAR) were tabulated along with a new summary metric called the average false alarm rate (AFAR). Some additional summary metrics are also introduced. Impact of the number of basis vectors in the target and background subspaces on detector performance was also investigated. For the given AVIRIS data set, the MaxD method as applied to the background subspace outperformed the other two methods tested (SVD and PPI)

Target Detection in a Structured Background Environment Using an Infeasibility Metric in an Invariant Space

This paper develops a hybrid target detector that incorporates structured backgrounds and physics based modeling together with a geometric infeasibility metric. More often than not, detection algorithms are usually 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. Background spaces are modeled using a linear subspace (structured) approach characterized by endmembers found by using the maximum distance method (MaxD). After augmenting the image data with the target space, 15 endmembers were found, which were not related to the target (i.e., background endmembers). A geometric infeasibility metric is developed which enables one to be more selective in rejecting false alarms. Preliminary results in the design of such a metric show that an orthogonal projection operator based on target space vectors can distinguish between target and background pixels. Furthermore, when used in conjunction with an operator that produces abundance-like values, we obtained separation between target, ackground, and anomalous pixels. This approach was applied to HYDICE image spectrometer data

Identification and Detection of Gaseous Effluents from Hyperspectral Imagery Using Invariant Algorithms

The ability to detect and identify effluent gases is, and will continue to be, of great importance. This would not only aid in the regulation of pollutants but also in treaty enforcement and monitoring the production of weapons. Considering these applications, finding a way to remotely investigate a gaseous emission is highly desirable. This research utilizes hyperspectral imagery in the infrared region of the electromagnetic spectrum to evaluate an invariant method of detecting and identifying gases within a scene. The image is evaluated on a pixel-by-pixel basis and is studied at the subpixel level. A library of target gas spectra is generated using a simple slab radiance model. This results in a more robust description of gas spectra which are representative of real-world observations. This library is the subspace utilized by the detection and identification algorithms. The subspace will be evaluated for the set of basis vectors that best span the subspace. The Lee algorithm will be used to determine the set of basis vectors, which implements the Maximum Distance Method (MaxD). A Generalized Likelihood Ratio Test (GLRT) determines whether or not the pixel contains the target. The target can be either a single species or a combination of gases. Synthetically generated scenes will be used for this research. This work evaluates whether the Lee invariant algorithm will be effective in the gas detection and identification problem

A subpixel target detection algorithm for hyperspectral imagery

The goal of this research is to develop a new algorithm for the detection of subpixel scale target materials on the hyperspectral imagery. The signal decision theory is typically to decide the existence of a target signal embedded in the random noise. This implies that the detection problem can be mathematically formalized by signal decision theory based on the statistical hypothesis test. In particular, since any target signature provided by airborne/spaceborne sensors is embedded in a structured noise such as background or clutter signatures as well as broad band unstructured noise, the problem becomes more complicated, and particularly much more under the unknown noise structure. The approach is based on the statistical hypothesis method known as Generalized Likelihood Ratio Test (GLRT). The use of GLRT requires estimating the unknown parameters, and assumes the prior information of two subspaces describing target variation and background variation respectively. Therefore, this research consists of two parts, the implementation of GLRT and the characterization of two subspaces through new approaches. Results obtained from computer simulation, HYDICE image and AVI RIS image show that this approach is feasible

Physics-Based Detection of Subpixel Targets in Hyperspectral Imagery

Hyperspectral imagery provides the ability to detect targets that are smaller than the size of a pixel. They provide this ability by measuring the reflection and absorption of light at different wavelengths creating a spectral signature for each pixel in the image. This spectral signature contains information about the different materials within the pixel; therefore, the challenge in subpixel target detection lies in separating the target's spectral signature from competing background signatures. Most research has approached this problem in a purely statistical manner. Our approach fuses statistical signal processing techniques with the physics of reflectance spectroscopy and radiative transfer theory. Using this approach, we provide novel algorithms for all aspects of subpixel detection from parameter estimation to threshold determination. Characterization of the target and background spectral signatures is a key part of subpixel detection. We develop an algorithm to generate target signatures based on radiative transfer theory using only the image and a reference signature without the need for calibration, weather information, or source-target-receiver geometries. For background signatures, our work identifies that even slight estimation errors in the number of background signatures can severely degrade detection performance. To this end, we present a new method to estimate the number of background signatures specifically for subpixel target detection. At the core of the dissertation is the development of two hybrid detectors which fuse spectroscopy with statistical hypothesis testing. Our results show that the hybrid detectors provide improved performance in three different ways: insensitivity to the number of background signatures, improved detection performance, and consistent performance across multiple images leading to improved receiver operating characteristic curves. Lastly, we present a novel adaptive threshold estimate via extreme value theory. The method can be used on any detector type - not just those that are constant false alarm rate (CFAR) detectors. Even on CFAR detectors our proposed method can estimate thresholds that are better than theoretical predictions due to the inherent mismatch between the CFAR model assumptions and real data. Additionally, our method works in the presence of target detections while still estimating an accurate threshold for a desired false alarm rate

Improving Hyperspectral Subpixel Target Detection Using Hybrid Detection Space

A Hyper-Spectral Image (HSI) has high spectral and low spatial resolution. As a result, most targets exist as subpixels, which pose challenges in target detection. Moreover, limitation of target and background samples always hinders the target detection performance. In this thesis, a hybrid method for subpixel target detection of an HSI using minimal prior knowledge is developed. The Matched Filter (MF) and Adaptive Cosine Estimator (ACE) are two popular algorithms in HSI target detection. They have different advantages in differentiating target from background. In the proposed method, the scores of MF and ACE algorithms are used to construct a hybrid detection space. First, some high abundance target spectra are randomly picked from the scene to perform initial detection to determine the target and background subsets. Then, the reference target spectrum and background covariance matrix are improved iteratively, using the hybrid detection space. As the iterations continue, the reference target spectrum gets closer and closer to the central line that connects the centers of target and background and resulting in noticeable improvement in target detection. Two synthetic datasets and two real datasets are used in the experiments. The results are evaluated based on the mean detection rate, Receiver Operating Characteristic (ROC) curve and observation of the detection results. Compared to traditional MF and ACE algorithms with Reed-Xiaoli Detector (RXD) background covariance matrix estimation, the new method shows much better performance on all four datasets. This method can be applied in environmental monitoring, mineral detection, as well as oceanography and forestry reconnaissance to search for extremely small target distribution in a large scene

Estimating the number of endmembers in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm.

This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images

MSDH: matched subspace detector with heterogeneous noise

The matched subspace detector (MSD) is a classical subspace-based method for hyperspectral subpixel target detection. However, the model assumes that noise has the same variance over different bands, which is usually unrealistic in practice. In this letter, we relax the equal variance assumption and propose a matched subspace detector with heterogeneous noise (MSDH). In essence, the noise variances are different for different bands and they can be estimated by using iteratively reweighted least squares methods. Experiments on two benchmark real hyperspectral datasets demonstrate the superiority of MSDH over MSD for subpixel target detection

Detection and identification of effluent gases using invariant hyperspectral algorithms

The ability to detect and identify effluent gases is a problem that has been pursued with limited success. An algorithm to do this would not only aid in the regulation of pollutants but also in treaty enforcement. Considering these applications, finding a way to remotely investigate a gaseous emission is highly desirable. This research utilizes hyperspectral imagery in the infrared region of the electromagnetic spectrum to evaluate invariant methods of detecting and identifying gases within a scene. The image is evaluated on a pixel-by-pixel basis and is also studied at the subpixel level. A library of target gas spectra is generated using a simple radiance model. This results in a more robust representation of the gas spectra which are representative of real-world observations. This library is the subspace utilized by the detection and identification algorithm. An evaluation was carried out to determine the subset of basis vectors that best span the subspace. Two basis vector selection methods are used to determine the subset of basis vectors; Singular Value Decomposition (SVD) and the Maximum Distance Method (MaxD). The Generalized Likelihood Ratio Test (GLRT) was used to determine whether the pixel is more like the target or the background. The target can be either a single species or a combination of gases, however, this study only looks for one gas at a time. Synthetically generated hyperspectral scenes in the longwave infrared (LWIR) region of the electromagnetic spectrum are used for this research. The test scenarios used in this study represented strong and weak plumes with single or multiple gas releases. In this work, strong and weak plumes refer to the release, which is on the order of tens of grams per second and tenths of grams per second, respectively. This work demonstrates the effectiveness of these invariant algorithms for the gas detection and identification problem

Using Lidar to geometrically-constrain signature spaces for physics-based target detection

A fundamental task when performing target detection on spectral imagery is ensuring that a target signature is in the same metric domain as the measured spectral data set. Remotely sensed data are typically collected in digital counts and calibrated to radiance. That is, calibrated data have units of spectral radiance, while target signatures in the visible regime are commonly characterized in units of re°ectance. A necessary precursor to running a target detection algorithm is converting the measured scene data and target signature to the same domain. Atmospheric inversion or compensation is a well-known method for transforming mea- sured scene radiance values into the re°ectance domain. While this method may be math- ematically trivial, it is computationally attractive and is most e®ective when illumination conditions are constant across a scene. However, when illumination conditions are not con- stant for a given scene, signi¯cant error may be introduced when applying the same linear inversion globally. In contrast to the inversion methodology, physics-based forward modeling approaches aim to predict the possible ways that a target might appear in a scene using atmospheric and radiometric models. To fully encompass possible target variability due to changing illumination levels, a target vector space is created. In addition to accounting for varying illumination, physics-based model approaches have a distinct advantage in that they can also incorporate target variability due to a variety of other sources, to include adjacency target orientation, and mixed pixels. Increasing the variability of the target vector space may be beneficial in a global sense in that it may allow for the detection of difficult targets, such as shadowed or partially concealed targets. However, it should also be noted that expansion of the target space may introduce unnecessary confusion for a given pixel. Furthermore, traditional physics-based approaches make certain assumptions which may be prudent only when passive, spectral data for a scene are available. Common examples include the assumption of a °at ground plane and pure target pixels. Many of these assumptions may be attributed to the lack of three-dimensional (3D) spatial information for the scene. In the event that 3D spatial information were available, certain assumptions could be levied, allowing accurate geometric information to be fed to the physics-based model on a pixel- by-pixel basis. Doing so may e®ectively constrain the physics-based model, resulting in a pixel-specific target space with optimized variability and minimized confusion. This body of work explores using spatial information from a topographic Light Detection and Ranging (Lidar) system as a means to enhance the delity of physics-based models for spectral target detection. The incorporation of subpixel spatial information, relative to a hyperspectral image (HSI) pixel, provides valuable insight about plausible geometric con¯gurations of a target, background, and illumination sources within a scene. Methods for estimating local geometry on a per-pixel basis are introduced; this spatial information is then fed into a physics-based model to the forward prediction of a target in radiance space. The target detection performance based on this spatially-enhanced, spectral target space is assessed relative to current state-of-the-art spectral algorithms