Binary partition trees-based robust adaptive hyperspectral RX anomaly detection

International audienceThe Reed-Xiaoli (RX) is considered as the benchmark algorithm in multidimensional anomaly detection (AD). However, the RX detector performance decreases when the statistical parameters estimation is poor. This could happen when the background is non-homogeneous or the noise independence assumption is not fulfilled. For a better performance, the statistical parameters are estimated locally using a sliding window approach. In this approach, called adaptive RX, a window is centered over the pixel under the test (PUT), so the background mean and covariance statistics are estimated us- ing the data samples lying inside the window's spatial support, named the secondary data. Sometimes, a smaller guard window prevents those pixels close to the PUT to be used, in order to avoid the presence of outliers in the statistical estimation. The size of the window is chosen large enough to ensure the invertibility of the covariance matrix and small enough to justify both spatial and spectral homogeneity. We present here an alternative methodology to select the secondary data for a PUT by means of a binary partition tree (BPT) representation of the image. We test the proposed BPT-based adaptive hyperspectral RX AD algorithm using a real dataset provided by the Target Detection Blind Test project

Graph Laplacian for Image Anomaly Detection

Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection; however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed; leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.Comment: Published in Machine Vision and Applications (Springer

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

Modeling and performance estimation for airborne minefield detection system

Many programs aimed at airborne mine and minefield detection are being pursued and different algorithms are being developed and evaluated to achieve performance specifications. Thus far, no single algorithm or detection architecture has been able to fulfill the performance specifications for different mine and minefield detection scenarios...a need exists for a simulation based approach. One such simulation system is developed and evaluated in this thesis. The factors affecting the performance of an airborne detection system include physical parameters (type of background, time of day), data collection parameters (swath width, number of steps, in-step and in-flight overlap), and minefield scenarios. Data collection parameters are included in the simulation tool. False alarms and mine statistics are modeled based on the available data collected as a part of the developmental programs. Various mine and minefield detection algorithms are modeled and evaluated. Simulations are run, and Receiver Operating Characteristic (ROC) curves are used to evaluate the performance at both the mine and minefield levels. Analytical models for minefield detection performance are formulated and used to validate the simulated performance --Abstract, page iii

Reconstruction Error and Principal Component Based Anomaly Detection in Hyperspectral imagery

The rapid expansion of remote sensing and information collection capabilities demands methods to highlight interesting or anomalous patterns within an overabundance of data. This research addresses this issue for hyperspectral imagery (HSI). Two new reconstruction based HSI anomaly detectors are outlined: one using principal component analysis (PCA), and the other a form of non-linear PCA called logistic principal component analysis. Two very effective, yet relatively simple, modifications to the autonomous global anomaly detector are also presented, improving algorithm performance and enabling receiver operating characteristic analysis. A novel technique for HSI anomaly detection dubbed multiple PCA is introduced and found to perform as well or better than existing detectors on HYDICE data while using only linear deterministic methods. Finally, a response surface based optimization is performed on algorithm parameters such as to affect consistent desired algorithm performance

Linear models, signal detection, and the Grassmann manifold

2014 Fall.Standard approaches to linear signal detection, reconstruction, and model identification problems, such as matched subspace detectors (MF, MDD, MSD, and ACE) and anomaly detectors (RX) are derived in the ambient measurement space using statistical methods (GLRT, regression). While the motivating arguments are statistical in nature, geometric interpretations of the test statistics are sometimes developed after the fact. Given a standard linear model, many of these statistics are invariant under orthogonal transformations, have a constant false alarm rate (CFAR), and some are uniformly most powerful invariant (UMPI). These properties combined with the simplicity of the tests have led to their widespread use. In this dissertation, we present a framework for applying real-valued functions on the Grassmann manifold in the context of these same signal processing problems. Specifically, we consider linear subspace models which, given assumptions on the broadband noise, correspond to Schubert varieties on the Grassmann manifold. Beginning with increasing (decreasing) or Schur-convex (-concave) functions of principal angles between pairs of points, of which the geodesic and chordal distances (or probability distribution functions) are examples, we derive the associated point-to-Schubert variety functions and present signal detection and reconstruction algorithms based upon this framework. As a demonstration of the framework in action, we implement an end-to-end system utilizing our framework and algorithms. We present results of this system processing real hyperspectral images

Detection algorithms for spatial data

This dissertation addresses the problem of anomaly detection in spatial data. The problem of landmine detection in airborne spatial data is chosen as the specific detection scenario. The first part of the dissertation deals with the development of a fast algorithm for kernel-based non-linear anomaly detection in the airborne spatial data. The original Kernel RX algorithm, proposed by Kwon et al. [2005a], suffers from the problem of high computational complexity, and has seen limited application. With the aim to reduce the computational complexity, a reformulated version of the Kernel RX, termed the Spatially Weighted Kernel RX (SW-KRX), is presented. It is shown that under this reformulation, the detector statistics can be obtained directly as a function of the centered kernel Gram matrix. Subsequently, a methodology for the fast computation of the centered kernel Gram matrix is proposed. The key idea behind the proposed methodology is to decompose the set of image pixels into clusters, and expediting the computations by approximating the effect of each cluster as a whole. The SW-KRX algorithm is implemented for a special case, and comparative results are compiled for the SW-KRX vis-à-vis the RX anomaly detector. In the second part of the dissertation, a detection methodology for buried mine detection is presented. The methodology is based on extraction of color texture information using cross-co-occurrence features. A feature selection methodology based on Bhattacharya coefficients and principal feature analysis is proposed and detection results with different feature-based detectors are presented, to demonstrate the effectiveness of the proposed methodology in the extraction of useful discriminatory information --Abstract, page iii

Target Detection Performance Bounds in Compressive Imaging

This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches accommodate signals of different strengths contaminated by a colored Gaussian background, and perform detection without reconstructing the underlying signals from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets coming from a known dictionary. The anomaly detector is designed to control the number of false discoveries. The proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the distance preservation property of the measurement matrix. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.Comment: Submitted to the EURASIP Journal on Advances in Signal Processin

Characterization of the spectral distribution of hyperspectral imagery for improved exploitation

Widely used methods of target, anomaly, and change detection when applied to spectral imagery provide less than desirable results due to the complex nature of the data. In the case of hyperspectral data, dimension reduction techniques are employed to reduce the amount of data used in the detection algorithms in order to produce better results and/or decreased computation time. This essentially ignores a significant amount of the data collected in k unique spectral bands. Methods presented in this work explore using the distribution of the collected data in the full k dimensions in order to identify regions of interest contained in spatial tiles of the scene. Here, interest is defined as small and large scale manmade activity. The algorithms developed in this research are primarily data driven with a limited number of assumptions. These algorithms will individually be applied to spatial subsets or tiles of the full scene to indicate the amount of interest contained. Each tile is put through a series of tests using the algorithms based on the full distribution of the data in the hyperspace. The scores from each test will be combined in such a way that each tile is labeled as either interesting or not interesting. This provides a cueing mechanism for image analysts to visually inspect locations within a hyperspectral scene with a high likelihood of containing manmade activity