Colin C. Olson

Abu Hasnat Mohammad Rubaiyat, Jordan Vincent, Colin Olson

Hyperspectral anomaly detection (HAD), a crucial approach for many civilian and military applications, seeks to identify pixels with spectral signatures that are anomalous relative to a preponderance of background signatures. Significant effort has been made to improve HAD techniques, but challenges arise due to complex real-world environments and, by definition, limited prior knowledge of potential signatures of interest. This paper introduces a novel HAD method by proposing a transport-based mathematical model to describe the pixels comprising a given hyperspectral image. In this approach, hyperspectral pixels are viewed as observations of a template pattern undergoing unknown deformations that enables their representation in the signed cumulative distribution transform (SCDT) domain. An unsupervised subspace modeling technique is then used to construct a model of abundant background signals in this domain, whereupon anomalous signals are detected as deviations from the learned model. Comprehensive evaluations across five distinct datasets illustrate the superiority of our approach compared to state-of-the-art methods.

Ratna Khatri, Anthony Kolshorn, Colin Olson et al.

This paper presents a novel, mathematically rigorous framework for autoencoder-type deep neural networks that combines optimal control theory and low-rank tensor methods to yield memory-efficient training and automated architecture discovery. The learning task is formulated as an optimization problem constrained by differential equations representing the encoder and decoder components of the network and the corresponding optimality conditions are derived via a Lagrangian approach. Efficient memory compression is enabled by approximating differential equation solutions on low-rank tensor manifolds using an adaptive explicit integration scheme. These concepts are combined to form OCTANE (Optimal Control for Tensor-based Autoencoder Network Emergence) -- a unified training framework that yields compact autoencoder architectures, reduces memory usage, and enables effective learning, even with limited training data. The framework's utility is illustrated with application to image denoising and deblurring tasks and recommendations regarding governing hyperparameters are provided.

Tegan Emerson, Sarah Tymochko, George Stantchev et al.

Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the scene. Moreover, this lack of spatial information also disqualifies the use of most state-of-the-art deep learning image-based classifiers. Here, we use characteristics of target tracks extracted from video sequences as data from which to derive distinguishing topological features that help robustly differentiate targets of interest from confusers. In particular, we calculate persistent homology from time-delayed embeddings of dynamic statistics calculated from motion tracks extracted from a wide field-of-view video stream. In short, we use topological methods to extract features related to target motion dynamics that are useful for classification and disambiguation and show that small targets can be detected at range with high probability.