Advancing Deep Learning for Data and Signal Processing Applications

Abstract

Modern sensing and information systems increasingly rely on deep learning to process high-dimensional data and signals, yet their deployment in real-world environments is constrained by several gaps: a lack of realistic, standardized benchmark datasets, architectures that do not fully exploit the structure of domain-specific data, slow or resource-inefficient training procedures, and a limited theoretical understanding of the fundamental limits of learning algorithms. This dissertation addresses these challenges by advancing deep learning methods, architectures, and theory for data and signal processing applications.We investigate these issues through a sequence of studies spanning adaptive radar processing, neural network architecture design, optimization methods, and information theory. We first use adaptive radar as a case study, showing that standard neural networks can perform accurate data-driven target localization, demonstrating the feasibility of deep learning for this class of signal processing problems. We then construct a large-scale, physics-based, complex-valued benchmark dataset for adaptive radar to enable systematic comparisons between classical space-time adaptive processing (STAP) methods and modern deep learning approaches, with extensions to real-world adaptive radar scenarios. To improve upon these approaches, we develop a novel neural network architecture tailored to complex-valued data that improves generalization and convergence. We propose two complementary mechanisms for accelerating training and improving generalization across these domains by adaptively integrating data via real-time class-wise error rates, and by exploiting the geometry of the underlying data distribution. Finally, we analyze the fundamental limits of generalization using autoencoders to derive a practical lower bound on generalization error.Altogether, our findings show that carefully designed datasets, architectures, and training objectives can substantially improve the efficacy of deep learning methods in data and signal processing applications. Our methods highlight the potential of using an integrated approach to deliver robust, reproducible performance in adaptive radar today, while laying a foundation for future data-driven systems that combine principled theoretical guarantees with empirical deep learning paradigms.