Loading...

WSS Graph Processes on Directed Graphs

Iraji, Mohammad Bagher | 2025

0 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58221 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Amini, Arash
  7. Abstract:
  8. In this thesis, we generalize the concepts of kernels, weak stationarity and white noise from undirected to directed graphs (digraphs) based on the Jordan decomposition of the shift operator. We characterize two types of kernels (type-I and type-II) and their corresponding localization operators for digraphs. We analytically study the interplay of these types of kernels with the concept of stationarity, specially the filtering properties. We also generalize graph Wiener filters and the related optimization framework to digraphs. For the special case of Gaussian processes, we show that the Wiener filtering again coincides with the MAP ‌estimator. We further investigate the linear minimum mean-squared error (LMMSE) estimator for the non-Gaussian cases; the corresponding optimization problem simplifies to a Lyapunov matrix equation. We propose an algorithm to solve the Wiener optimization using proximal splitting methods. Moreover, we provide simulation results to verify the provided theory. Finally, we study the stationarity of an AR graph process on a digraph using the proposed definition and we also propose the problem of stationary approximation of graph processes on undirected graphs and provide the obtained results about it
  9. Keywords:
  10. Graph Signal Processing ; Graph Fourier Transform ; Power Spectral Density (PSD)Analysis ; Directed Graph ; Wiener Filter

 Digital Object List

 Bookmark

...see more