Agenda

PhD Thesis Defence

• Thursday, 30 April 2026
• 12:30-13:30
• Aula Senaatszaal

Kronecker Compressed Sensing With Structured Sparsity

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 themultidimensional 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 sparsitymodels: 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.

First, for Kronecker-supported signals, we introduce Kronecker sparse Bayesian learning. To promote the Kronecker-supported sparsity, we adopt a Kronecker-structured prior in the sparse Bayesian learning framework. Such a prior leads to a nonconvex optimization problem, which is solved using an alternating-minimization method with convergence guarantee and a singular value decomposition-based variant that attains competitive accuracy with lower computation time. The analysis further shows that encoding the Kronecker support reduces undesirable local minima, attributing to the improved performance. We test our algorithms on the channel estimation problem for intelligent reflecting surface-aided systems, showing better performance and efficiency.

Second, for Kronecker-structured signals where the sparse vector itself can be factorized across multiple dimensions, we develop a decomposition-based recovery that breaks the high-dimensional problem into multiple lower-dimensional subproblems. Furthermore, in the context of basis expansion model for unknown parameter estimation, we design an off-grid sparse Bayesian learning tomitigate grid mismatch. Theoretical results guarantee the error bound of the decomposition step, explain the denoising effect which we attribute to improved performance, and provide convergence guarantees for our off-grid method.We test our algorithms on the channel estimation problem for intelligent reflecting surface-aided systems in the off-grid setting, showing not only significant performance gains but also improved accuracy for off-grid angle estimation.

Third, moving beyond structure-specific designs, we further present a hierarchical multi-stage framework that reframes the Kronecker compressed sensing problem as a sequence of dimension-wise subproblems. This yields a unified algorithmic framework that can be combined with any sparse recovery algorithm, and are capable of handling standard, hierarchical, and Kronecker-supported sparsity patterns.We demonstrate its practical utility in both wireless communications and video sequence reconstruction, showing competitive performance with reduced computational cost.

Overall, thework offers practical tools and insights for Kronecker compressed sensing by coupling structure-aware algorithms with rigorous guarantees and realistic applications

Overview of PhD Thesis Defence