Andrew M. Fraser

Statistical Reconstruction for Cosmic Ray Muon Tomography

Highly penetrating cosmic ray muons constantly shower the earth at a rate of about 1 muon per cm2 per minute. We have developed a technique which exploits the multiple Coulomb scattering of these particles to perform nondestructive inspection without the use of artificial radiation. In prior work , we have described heuristic methods for processing muon data to create reconstructed images. In this paper, we present a maximum likelihood/expectation maximization tomographic reconstruction algorithm designed for the technique. This algorithm borrows much from techniques used in medical imaging, particularly emission tomography, but the statistics of muon scattering dictates differences. We describe the statistical model for multiple scattering, derive the reconstruction algorithm, and present simulated examples. We also propose methods to improve the robustness of the algorithm to experimental errors and events departing from the statistical model.

Tomographic Imaging with Cosmic Ray Muons

Over 120 million vehicles enter the United States each year. Many are capable of transporting hidden nuclear weapons or nuclear material. Currently deployed X-ray radiography systems are limited because they cannot be used on occupied vehicles and the energy and dose are too low to penetrate many cargos. We present a new technique that overcomes these limitations by obtaining tomographic images using the multiple scattering of cosmic radiation as it transits each vehicle. When coupled with passive radiation detection, muon interrogation could contribute to safe and robust border protection against nuclear devices or material in occupied vehicles and containers.

Wide-Area Motion Imagery

Wide-area motion imagery (WAMI) sensors are placed on helicopters, balloons, small aircraft, or unmanned aerial vehicles and are used to image small city-sized areas at approximately 0.5 m/pixel and about one or two frames/s. The geospatial-temporal data sets produced by these systems allow for the observation of many dynamic phenomena that were previously inaccessible in street-level video data, but the efficient exploitation of this data poses significant technical challenges for image and video analysis and for data mining. Content of interest is defined in very abstract terms related to how humans interpret video imagery, but the data is defined in very physical terms related to the imaging device. This difference in representations is often called the semantic gap. In this review article, we describe advances that have been made and the advances that will be needed to produce the hierarchy of computational models required to narrow the semantic gap in WAMI.

Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery

To detect weak signals on cluttered backgrounds in high dimensional spaces (such as gaseous plumes in hyperspectral imagery) without excessive false alarms requires that the background clutter be effectively characterized. If the clutter is Gaussian, the well-known linear matched filter optimizes the sensitivity to a given plume signal while suppressing the effect of the background clutter. In practice, the background clutter is rarely Gaussian. Here we illustrate non-linear corrections to the matched filter that are optimal for two non-Gaussian clutter models and we report on parametric and nonparametric characterizations of background clutter.

Optimizing the Tracking Efficiency for Cosmic Ray Muon Tomography

We have built a detector capable of locating high Z objects in the sampling (middle) region of the detector. As atomic number increases, radiation length rapidly decreases, yielding larger variance in scattering angle. Cosmic ray muon tomography works by tracking muons above the sampling region, and tracking them below the region as well. The difference between the two trajectories yield information, via the muon scattering variance, of the materials contained within the sampling region [Borozdin, K, et al., 2003]. One of most important aspects of cosmic ray tomography is minimizing exposure time. The cosmic ray flux is about 1 cm-2 min-1, and the goal is to use them for detecting high-density materials as quickly as possible. This involves using all of the information possible to reconstruct tracks with redundant detectors. Detector scattering residuals yield a low precision measurement of muon energy. Knowing the rough energy of an incoming particle will yield more precisely the expected scattering variance (currently the expectation value of ~3 GeV is used).

Decision boundaries in two dimensions for target detection in hyperspectral imagery.

We present an approach to the problems of weak plume detection and sub-pixel target detection in hyperspectral imagery that operates in a two-dimensional space. In this space, one axis is a matched-filter projection of the data and the other axis is the magnitude of the residual after matched-filter subtraction. Although it is only two-dimensional, this space is rich enough to include several well-known signal detection algorithms, including the adaptive matched filter, the adaptive coherence estimator, and the finite-target matched filter. Because this space is only two-dimensional, adaptive machine learning methods can produce new plume detectors without being stymied by the curse of dimensionality. We investigate, in particular, the utility of the support vector machine for learning boundaries in this matched-filter-residual space, and compare the performance of the resulting nonlinearly adaptive detector to well-known alternatives.

Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter

For known signals that are linearly superimposed on gaussian backgrounds, the linear adaptive matched filter (AMF) is well-known to be the optimal detector. The AMF has furthermore proved to be remarkably effective in a broad range of circumstances where it is not optimal, and for which the optimal detector is not linear. In these cases, nonlinear detectors are theoretically superior, but direct estimation of nonlinear detectors in high-dimensional spaces often leads to flagrant overfitting and poor out-of-sample performance. Despite this difficulty in the general case, we will describe several situations in which nonlinearity can be effectively combined with the AMF to detect weak signals. This allows improvement over AMF performance while avoiding the full force of dimensionalitys curse.

Information extraction for muon radiography

The paths of muons traveling through matter are affected by Coulomb multiple scattering. The magnitude of that interaction depends on the radiation length of the traversed medium, with high-Z matter scattering more than low-Z matter. The net effect on the path of a muon through an object is both a change in the direction and an orthogonal displacement orthogonal. Both these quantities can be measured experimentally for individual muons, opening the possibility of tomographic reconstruction of the radiation lengths of unknown complex objects. We present a framework to characterize the ability to reconstruct the scattering density from muon scattering data for detecting and locating areas of high Z material. Our analysis shows the importance of having detectors with large aperture, and the importance of using both the change in angle and displacement

Incorporating invariants in Mahalanobis distance based classifiers: application to face recognition

We present a technique for combining prior knowledge about transformations that should be ignored with a covariance matrix estimated from training data to make an improved Mahalanobis distance classifier. Modern classification problems often involve objects represented by high-dimensional vectors or images (for example, sampled speech or human faces). The complex statistical structure of these representations is often difficult to infer from the relatively limited training data sets that are available in practice. Thus, we wish to efficiently utilize any available a priori information, such as transformations or the representations with respect to which the associated objects are known to retain the same classification (for example, spatial shifts of an image of a handwritten digit do not alter the identity of the digit). These transformations, which are often relatively simple in the space of the underlying objects, are usually nonlinear in the space of the object representation, making their inclusion within the framework of a standard statistical classifier difficult. Motivated by prior work of Simard et al. (1998; 2000), we have constructed a new classifier which combines statistical information from training data and linear approximations to known invariance transformations. When tested on a face recognition task, performance was found to exceed by a significant margin that of the best algorithm in a reference software distribution.

Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery

When a matched filter is used for detecting a weak target in a cluttered background (such as a gaseous plume in a hyperspectral image), it is important that the background clutter be well-characterized. A statistical characterization can be obtained from the off-plume pixels of a hyperspectral image, but if on-plume pixels are inadvertently included, then that background characterization will be contaminated. In broad area search scenarios, where detection is the central aim, it is by definition unknown which pixels in the scene are off-plume, so some contamination is inevitable. In general, the contaminated background degrades the ability of the matched-filter to detect that signal. This could be a practical problem in plume detection. A linear analysis suggests that the effect is limited, and actually vanishes in some cases. In this study, we take into account the Beers Law nonlinearity of plume absorption, and we investigate the effect of that nonlinearity on the signal contamination.