Doctor of Philosophy, The Ohio State University, 2024, Electrical and Computer Engineering

This dissertation addresses two distinct topics: inference from synthetic aperture radar (SAR) data and the application of lattice theory to array signal processing. First, we propose a series of methods that mitigate the effect of speckle in inference tasks involving multichannel SAR data. Coherent imaging methods like SAR are subject to speckle, and the suppression of this noise-like quality is often a prerequisite to image interpretation. We propose a technique that recovers the per-pixel multichannel SAR covariance matrix and incorporates a statistical model of speckle and a priori knowledge of the varieties of clutter present in the scene. In this approach, an expectation-maximization algorithm is made computationally tractable by a graph-coloring probing technique. We next address the problem of coherent change detection in repeat-pass SAR data. A Bayesian change detection approach is given that assigns prior distributions to the unobserved model variables to exploit spatial structure both in the geophysical scattering qualities of the scene and among the scene disturbances that take place between the passes. We also give a polarimetric SAR (PolSAR) despeckling method based on convolutional neural networks (CNNs). An invertible transformation involving a matrix logarithm is used to facilitate CNN processing of the PolSAR data. A residual learning strategy is adopted, in which the CNN is trained to identify the speckle component which is then removed from the corrupted image. The latter portion of this dissertation is concerned with the application of lattice theory to array signal processing. We consider the problem of maximum likelihood parameter estimation in mixed integer linear models and provide two polynomial-time solution methods for special cases of this problem. These approaches extend the prior art by allowing for multivariate real-valued unknowns and more general linear models. We then provide a generally applicable alternative so (open full item for complete abstract)

Committee: Lee Potter (Advisor); Kiryung Lee (Committee Member); Emre Ertin (Committee Member) Subjects: Electrical Engineering; Engineering