Optimization based models for explainable deep learning architectures in multidimensional signal processing applications
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Date
2024-09-26
Authors
Γκίλλας, Αλέξανδρος
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Abstract
Multidimensional signals are found in many important fields, including remote sensing, precision agriculture, autonomous robotic systems, and complex recommendation systems. These signals often represent rich and structured information about physical phenomena, environmental conditions, or user behaviors. To address challenges in processing and analyzing these signals, we introduce a framework based on three layers of dependencies. The first layer considers data-level dependencies within the multidimensional signals themselves. The second layer examines domain-level dependencies among the areas where these signals originate or are applied. The third layer focuses on agent-level dependencies between a network of agents processing such signals and share a common goal. Modeling these interconnected layers of dependencies can provide critical insights and enhance performance in tasks such as spectral and LiDAR super-resolution and cross-domain recommendation, ultimately improving the accuracy and efficiency of multidimensional signal processing across diverse applications.In recent years, deep learning-based solutions have become common for processing multidimensional signals. However, these approaches seem to have reached a performance ceiling, with deeper architectures being proposed by trial and error, lacking clear mathematical justification, and requiring increasingly larger datasets for training. This dissertation argues that by utilizing optimization theory, we can more effectively leverage these three layer-dependencies, resulting in solutions that are both explainable and efficient. For data-level dependencies, we developed novel optimization problems employing appropriate learnable or handcrafted regularizers, grounded in optimization theory, such as sparse representation theory. By leveraging these principles, we develop advanced algorithms that capture intricate dependencies within the data, leading to efficient iterative solutions. Building on deep unrolling and deep equilibrium approaches, we enhance these solutions by developing novel explainable deep learning architectures for solving the proposed optimization problems, designed to tackle a wide range of image processing applications, such as hyperspectral denoising and deconvolution.In scenarios where multidimensional signals originate from different domains, additional dependencies between these domains can be considered, increasing the effectiveness of the previously mentioned approaches. To utilize the domain-level dependencies, we develop coupled domain or domain adaptation methodologies based on novel frameworks with coupled dictionaries, coupled autoencoders, and deep unrolling. These create explainable solutions for problems such as spectral super-resolution in precision agriculture, LiDAR super-resolution in the automotive domain, and cross-domain recommendation. By discovering and utilizing transfer functions between domains, we enable high-quality signal reconstruction and effective knowledge transfer across related domains.Furthermore, in this dissertation, we extend the capabilities of the proposed methodologies, arguing that in many real-world scenarios, such as autonomous driving, networks of agents collaboratively processing and learning from multidimensional data. For agent-level dependencies, we explore federated learning to enable collaborative processing while ensuring data privacy and computational efficiency. We investigate resource-efficient federated deep equilibrium and unrolling models, particularly suitable for scenarios with heterogeneous devices, applied to tasks such as LiDAR super-resolution and medical imaging.Overall, this study provides a novel connection between mathematically solid and extensively studied optimization approaches, such as sparse representation modeling, and modern deep learning methods. By integrating these approaches, this work offers explainable, efficient solutions for complex multidimensional signal processing tasks. The contributions advance the state-of-the-art in remote sensing, precision agriculture, autonomous systems, and complex recommendation systems, with potential implications for a wide range of real-world scenarios. This dissertation bridges the gap between theoretical optimization techniques and practical deep learning models, setting a foundation for future innovations in multidimensional signal processing.
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Keywords
Εxplainable deep learning, Optimization theory, Sparse representation theory, Federated learning