Timothy Doster

A parametric study of unsupervised anomaly detection performance in maritime imagery using manifold learning techniques

We investigate the parameters that govern an unsupervised anomaly detection framework that uses nonlinear techniques to learn a better model of the non-anomalous data. A manifold or kernel-based model is learned from a small, uniformly sampled subset in order to reduce computational burden and under the assumption that anomalous data will have little effect on the learned model because their rarity reduces the likelihood of their inclusion in the subset. The remaining data are then projected into the learned space and their projection errors used as detection statistics. Here, kernel principal component analysis is considered for learning the background model. We consider spectral data from an 8-band multispectral sensor as well as panchromatic infrared images treated by building a data set composed of overlapping image patches. We consider detection performance as a function of patch neighborhood size as well as embedding parameters such as kernel bandwidth and dimension. ROC curves are generated over a range of parameters and compared to RX performance.

Designing manufacturable filters for a 16-band plenoptic camera using differential evolution

A 16-band plenoptic camera allows for the rapid exchange of filter sets via a 4x4 filter array on the lenss front aperture. This ability to change out filters allows for an operator to quickly adapt to different locales or threat intelligence. Typically, such a system incorporates a default set of 16 equally spaced at-topped filters. Knowing the operating theater or the likely targets of interest it becomes advantageous to tune the filters. We propose using a modified beta distribution to parameterize the different possible filters and differential evolution (DE) to search over the space of possible filter designs. The modified beta distribution allows us to jointly optimize the width, taper and wavelength center of each single- or multi-pass filter in the set over a number of evolutionary steps. Further, by constraining the function parameters we can develop solutions which are not just theoretical but manufacturable. We examine two independent tasks: general spectral sensing and target detection. In the general spectral sensing task we utilize the theory of compressive sensing (CS) and find filters that generate codings which minimize the CS reconstruction error based on a fixed spectral dictionary of endmembers. For the target detection task and a set of known targets, we train the filters to optimize the separation of the background and target signature. We compare our results to the default 16 at-topped non-overlapping filter set which comes with the plenoptic camera and full hyperspectral resolution data which was previously acquired.

Machine learning approach to OAM beam demultiplexing via convolutional neural networks

Orbital angular momentum (OAM) beams allow for increased channel capacity in free-space optical communication. Conventionally, these OAM beams are multiplexed together at a transmitter and then propagated through the atmosphere to a receiver where, due to their orthogonality properties, they are demultiplexed. We propose a technique to demultiplex these OAM-carrying beams by capturing an image of the unique multiplexing intensity pattern and training a convolutional neural network (CNN) as a classifier. This CNN-based demultiplexing method allows for simplicity of operation as alignment is unnecessary, orthogonality constraints are loosened, and costly optical hardware is not required. We test our CNN-based technique against a traditional demultiplexing method, conjugate mode sorting, with various OAM mode sets and levels of simulated atmospheric turbulence in a laboratory setting. Furthermore, we examine our CNN-based technique with respect to added sensor noise, number of photon detections, number of pixels, unknown levels of turbulence, and training set size. Results show that the CNN-based demultiplexing method is able to demultiplex combinatorially multiplexed OAM modes from a fixed set with >99% accuracy for high levels of turbulence-well exceeding the conjugate mode demultiplexing method. We also show that this new method is robust to added sensor noise, number of photon detections, number of pixels, unknown levels of turbulence, and training set size.

Building robust neighborhoods for manifold learning-based image classification and anomaly detection

We exploit manifold learning algorithms to perform image classification and anomaly detection in complex scenes involving hyperspectral land cover and broadband IR maritime data. The results of standard manifold learning techniques are improved by including spatial information. This is accomplished by creating super-pixels which are robust to affine transformations inherent in natural scenes. We utilize techniques from harmonic analysis and image processing, namely, rotation, skew, flip, and shift operators to develop a more representational graph structure which defines the data-dependent manifold.

A Novel Detection Paradigm and Its Comparison to Statistical and Kernel-Based Anomaly Detection Algorithms for Hyperspectral Imagery

Detection of anomalous pixels within hyperspectral imagery is frequently used for purposes ranging from the location of invasive plant species to the detection of military targets. The task is unsupervised because no information about target or background spectra is known or assumed. Some of the most commonly used detection algorithms assume a statistical distribution for the background and rate spectral anomalousness based on measures of deviation from the statistical model; but such assumptions can be problematic because hyperspectral data rarely meet them. More recent algorithms have employed data-driven machine learning techniques in order to improve performance. Here we investigate a novel kernel-based method and show that it achieves top detection performance relative to seven other state-of-the-art methods on a commonly tested data set.

A study of anomaly detection performance as a function of relative spectral abundances for graph- and statistics-based detection algorithms

We investigate an anomaly detection framework that leverages manifold learning techniques to learn a background model. A manifold is learned from a small, uniformly sampled subset under the assumption that any anomalous samples will have little effect on the learned model. The remaining data are then projected into the manifold space and their projection errors used as detection statistics. We study detection performance as a function of the interplay between sub-sampling percentage and the abundance of anomalous spectra relative to background class abundances using synthetic data derived from field collects. Results are compared against both graph-based and traditional statistical models.

A study of the effect of alternative similarity measures on the performance of graph-based anomaly detection algorithms

We investigate an anomaly detection framework that uses manifold-based distances within the existing skeleton kernel principle component analysis (SkPCA) manifold-learning technique. SkPCA constructs a manifold from the an adjacency matrix built using a sparse subsample of the data and a similarity measure. In anomaly detection the relative abundance of the anomalous class is rare by definition and in practice anomalous samples are unlikely to be randomly selected for inclusion in the sparse data subsample. Thus, anomalies should not be well modeled by the SkPCA-constructed model. Here, we consider alternative distance measures based on viewing spectral pixels as points in projective space, that is, each pixel is a 1-dimensional line through the origin. Chordal and geodesic distances are computed between hyperspectral pixels and detection performance leveraging these distances is compared to alternative anomaly detection algorithms. In addition, we introduce Ensemble SkPCA which utilizes the ensemble of mean, normalized detection scores corresponding to multiple randomly generated skeletons. For acceptable false alarm tolerances, the ensemble detection score derived from chordaland geodesic-based methods achieves higher probability of detection than Euclidean distance-based Ensemble SkPCA or the benchmark RX algorithm.

Selecting an Optimized COTS Filter Set for Multispectral Plenoptic Sensing

A 16-band plenoptic camera allows for the rapid exchange of filter sets via a 4x4 filter array on the lens’s front aperture thus allowing an operator to quickly adapt to a different locale or threat intelligence. Typically, such a system incorporates a default set of 16 equally spaced, non-overlapping, flat-topped filters. Knowing the operating theater or the likely targets of interest it becomes advantageous to tune the filters; we propose a differential evolution approach to search over a set of commercial off-the-shelf (COTS) filters for an optimal collection of filters. We examine two independent tasks: general spectral sensing and target detection. For general spectral sensing, we utilize compressive sensing and find filters that generate codings which minimize the reconstruction error. For target detection, we select filters to optimize the separation between the background and a set of targets. We compare the results obtained using the selected COTS filters to the default filter set and full spectral resolution hyperspectral (HS) filter set for target detection and general spectral sensing on a previously obtained HS image.

An Overview of Numerical Acceleration Techniques for Nonlinear Dimension Reduction

We are living in an increasingly data-dependent world - making sense of large, high-dimensional data sets is an important task for researchers in academia, industry, and government. Techniques from machine learning, namely nonlinear dimension reduction, seek to organize this wealth of data by extracting descriptive features. These techniques, though powerful in their ability to find compact representational forms, are hampered by their high computational costs. In their naive implementation, this prevents them from processing large modern data collections in a reasonable time or with modest computational means. In this summary article we shall discuss some of the important numerical techniques which drastically increase the computational efficiency of these methods while preserving much of their representational power. Specifically, we address random projections, approximate k-nearest neighborhoods, approximate kernel methods, and approximate matrix decomposition methods.

OAM channel efficiency in the presence of turbulence for Laguerre- and Bessel-Gauss beams

Bessel-Gauss beams, a type of pseudo non-diffracting beam, are examined for their robustness for propagation through turbulent free space and compared to Laguerre-Gauss beams of various orders using an optical transformation sorting methods.