Hilbert Transform

The Hilbert transform is a mathematical operation that transforms a function into its analytical counterpart, revealing information about its frequency components and phase relationships. Current research focuses on its applications in diverse fields, including efficient data sampling and ordering (e.g., using Hilbert curves for improved landscape analysis and point cloud processing), advanced image reconstruction techniques in computed tomography (e.g., employing novel neural network architectures like OSNet and MNetO), and the analysis of complex spatio-temporal data (e.g., through extensions of principal component analysis in kernel Hilbert spaces). These advancements improve computational efficiency, enhance data analysis capabilities, and lead to more accurate and robust solutions in various scientific and engineering domains.