High-dimensional signal processing with manifolds and graphs

High-dimensional signals are ubiquitous, appearing across a wide range of domains, from sensor arrays to general tabular datasets, where each instance or measurement can be interpreted as a high-dimensional signal. In this talk, I will present advanced signal processing techniques for such data using tools from graph theory and manifold geometry. I will begin by addressing this problem in the context of Graph Signal Processing (GSP), which extends classical signal processing techniques to signals defined on irregular, graph-structured domains, and present a new functorial framework for comparing collections of graph signals that may lie on different or unknown graphs, thereby extending the current GSP setting. Next, I will show how this functorial perspective guides a novel approach to compress graphs while maintaining their key structural characteristics. Then, I will show how this functional perspective on graphs also provides a novel approach to reading intracranial EEG, enabling accurate detection, localization, and early prediction of epileptic seizures. Finally, I will describe a wideband direction-of-arrival estimation method that overcomes narrowband interference by exploiting the problem’s unique geometry.

Ph.D. student Under the supervision of Associate Prof. Ronen Talmon.