Publications

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Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More recent models also attempt to capture features such as fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data, whether due to numerical approximation or incomplete physics. In order to make realistic forecasts and improve understanding of the underlying processes, it is necessary to calibrate the numerical model to field data. Traditional calibration methods based on generalized least-square metrics are flawed for linear features such as sea ice cracks. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness, which involves optimally aligning model output with observed features using cutting-edge image registration techniques. This work can also have application to other physical models which produce coherent structures. Supplementary materials accompanying this paper appear online.

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We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phase variability, or handle it via preprocessing, that is, use an off–the–shelf technique for functional alignment and phase removal. We develop a functional principal component regression model which has a comprehensive approach in handling phase and amplitude variability. The model utilizes a mathematical representation of the data known as the square–root slope function. These functions preserve the L² norm under warping and are ideally suited for simultaneous estimation of regression and warping parameters. Furthermore, using both simulated and real–world data sets, we demonstrate our approach and evaluate its prediction performance relative to current models. In addition, we propose an extension to functional logistic and multinomial logistic regression.

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Our work in radiographic image matching has centered on the use of SURF (Speeded Up Robust Features) for feature detection, and FLANN (Fast Learning Artificial Neural Network) for feature matching. We discovered that while the SURF process does return information on location, scale, and rotation for each detected feature, they are not essential for image matching. The nature of the remaining feature detection data does not appear to contain any useful information in terms of reconstructing a useful portion of an image, and therefore is not amenable to reconstructing the original image. This led us to wonder if, in fact, we had discovered an irreversible process; the original image could not be constructed from the remaining feature data. Additional detail on the derivation of the image processing and matching algorithms and the irreversibility hypothesis are available in the final SAND Report documenting our previous LDRD work (SAND2015-9665 “Processing Radiation Images Behind an Information Barrier for Automatic Warhead Authentication” Little, Wilson, Weber and Novick, 2015).

In this paper, we consider the problem of denoising and classification of SONAR signals observed under compositional noise, i.e., they have been warped randomly along the x-axis. The traditional techniques do not account for such noise and, consequently, cannot provide a robust classification of signals. We apply a recent framework that: 1) uses a distance-based objective function for data alignment and noise reduction; and 2) leads to warping-invariant distances between signals for robust clustering and classification. We use this framework to introduce two distances that can be used for signal classification: a) a y-distance, which is the distance between the aligned signals; and b) an x-distance that measures the amount of warping needed to align the signals. We focus on the task of clustering and classifying objects, using acoustic spectrum (acoustic color), which is complicated by the uncertainties in aspect angles at data collections. Small changes in the aspect angles corrupt signals in a way that amounts to compositional noise. As a result, we demonstrate the use of the developed metrics in classification of acoustic color data and highlight improvements in signal classification over current methods.