Kronecker Compressed Sensing With Structured Sparsity
Algorithms, Guarantees, and Applications
Y. He (TU Delft - Signal Processing Systems)
A.J. van der Veen – Promotor (TU Delft - Signal Processing Systems)
G. Joseph – Copromotor (TU Delft - Signal Processing Systems)
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Abstract
This dissertation focuses on Kronecker compressed sensing, recovering multidimensional sparse signals from their linear projections on Kronecker product measurement matrices. Multidimensional signals are functions of different dimensions, each conveying a specific physical quantity and they arise in applications such as wireless communications and image processing. Kronecker product matrix naturally captures the multidimensional nature, making Kronecker compressed sensing a powerful framework for the recovery. Beyond the standard sparsity, practical signals typically have additional structures.We examine three structured sparsity models: hierarchical, Kronecker-supported, and Kronecker-structured. We start with algorithms and guarantees for the Kronecker-supported and Kronecker structured patterns, and then proceed to a unified algorithmic and theoretical framework, showing how leveraging structure in measurement matrices and sparsity patterns yields gains in accuracy and efficiency....