C. C. Olson

The Bispectrum and Bicoherence for Quadratically Nonlinear Systems Subject to Non-Gaussian Inputs

In the analysis of data from nonlinear systems both the bispectrum and the bicoherence have emerged as useful tools. Both are frequently used to detect the influence of a nonlinear system on the joint probability distribution of the system input. Previous work has provided an analytical expression for the bispectrum of a quadratically nonlinear system output if the input is stationary, jointly Gaussian distributed. This work significantly generalizes the previous analysis by providing an analytical expression for the bispectrum of the response of quadratically nonlinear systems subject to stationary, jointly non-Gaussian inputs possessing arbitrary auto-correlation function. The expression is then used to determine the optimal input probability density function for detecting a quadratic nonlinearity in a second-order system. It is also shown how the expression can be used to design an optimal nonlinear filter for detecting deviations from normality in the probability density of a signal.

Laser-induced thermophoresis of individual particles in a viscous liquid

This paper presents a detailed investigation of the motion of individual micro-particles in a moderately-viscous liquid in direct response to a local, laser-induced temperature gradient. By measuring particle trajectories in 3D, and comparing them to a simulated temperature profile, it is confirmed that the thermally-induced particle motion is the direct result of thermophoresis. The elevated viscosity of the liquid provides for substantial differences in the behavior predicted by various models of thermophoresis, which in turn allows measured data to be most appropriately matched to a model proposed by Brenner. This model is then used to predict the effective force resulting from thermophoresis in an optical trap. Based on these results, we predict when thermophoresis will strongly inhibit the ability of radiation pressure to trap nano-scale particles. The model also predicts that the thermophoretic force scales linearly with the viscosity of the liquid, such that choice of liquid plays a key role in the relative strength of the thermophoretic and radiation forces.

Characterization of the AWARE 10 two-gigapixel wide-field-of-view visible imager

System requirements for many military electro-optic and IR camera systems reflect the need for both wide-field-of-view situational awareness as well as high-resolution imaging for target identification. In this work we present a new imaging system architecture designed to perform both functions simultaneously and the AWARE 10 camera as an example at visible wavelengths. We first describe the basic system architecture and user interface followed by a laboratory characterization of the system optical performance. We then describe a field experiment in which the camera was used to identify several maritime targets at varying range. The experimental results indicate that users of the system are able to correctly identify ~10 m targets at between 4 and 6 km with 70% accuracy.

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.

Estimating detection and identification probabilities in maritime target acquisition

This work describes several approaches to the estimation of target detection and identification probabilities as a function of target range. A Bayesian approach to estimation is adopted, whereby the posterior probability distributions associated with these probabilities are analytically derived. The parameter posteriors are then used to develop credible intervals quantifying the degree of uncertainty in the parameter estimates. In our first approach we simply show how these credible intervals evolve as a function of range. A second approach, also following the Bayesian philosophy, attempts to directly estimate the parameterized performance curves. This second approach makes efficient use of the available data and yields a distribution of probability versus range curves. Finally, we demonstrate both approaches using experimental data collected from wide field-of-view imagers focused on maritime targets.

Manifold learning techniques for unsupervised anomaly detection

Abstract Appropriately identifying outlier data is a critical requirement in the decision-making process of many expert and intelligent systems deployed in a variety of fields including finance, medicine, and defense. Classical outlier detection schemes typically rely on the assumption that normal/background data of interest are distributed according to an assumed statistical model and search for data that deviate from that assumption. However, it is frequently the case that performance is reduced because the underlying distribution does not follow the assumed model. Manifold learning techniques offer improved performance by learning better models of the background but can be too computationally expensive due to the need to calculate a distance measure between all data points. Here, we study a general framework that allows manifold learning techniques to be used for unsupervised anomaly detection by reducing computational expense via a uniform random sampling of a small fraction of the data. A background manifold is learned from the sample and then an out-of-sample extension is used to project unsampled data into the learned manifold space and construct an anomaly detection statistic based on the prediction error of the learned manifold. The method works well for unsupervised anomaly detection because, by definition, the ratio of anomalous to non-anomalous data points is small and the sampling will be dominated by background points. However, a variety of parameters that affect detection performance are introduced so we use here a low-dimensional toy problem to investigate their effect on the performance of four learning algorithms (kernel PCA, two versions of diffusion map, and the Parzen density estimator). We then apply the methods to the detection of watercraft in an ensemble of 22 infrared maritime scenes where we find kernel PCA to be superior and show that it outperforms a commonly employed baseline algorithm. The framework is not limited to the tested image processing example and can be used for any unsupervised anomaly detection task.

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.

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.

Range performance of the DARPA AWARE wide field-of-view visible imager

In a prior paper, we described a new imaging architecture that addresses the need for wide field-of-view imaging combined with the resolution required to identify targets at long range. Over the last two years substantive improvements have been made to the system, both in terms of the size, weight, and power of the camera as well as to the optics and data management software. The result is an overall improvement in system performance, which we demonstrate via a maritime target identification experiment.

Automated detection of watercraft in short-wave infrared imagery

Abstract. An automated approach for detecting the presence of watercraft in a maritime environment characterized by regions of land, sea, and sky, as well as multiple targets and both water- and land-based clutter, is described. The detector correlates a wavelet model of previously acquired images with those obtained from newly acquired scenes. The resulting detection statistic outperforms two other detectors in terms of probability of detection for a given (low) false alarm rate. It is also shown how the detection statistics associated with different wavelet models can be combined in a way that offers still further improvements in performance. The approach is demonstrated to be effective in finding watercraft in previously collected short-wave infrared imagery.