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Stationary Processes on Directed Graphs

Iraji, M. B ; Sharif University of Technology | 2024

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  1. Type of Document: Article
  2. DOI: 10.1109/IWCIT62550.2024.10553092
  3. Publisher: 2024
  4. Abstract:
  5. In this paper, we extend the concepts of kernels, weak stationarity and white noise to the case of directed graphs (digraphs). We shall determine the attributes of two types of kernels (I and II) based on the Jordan decomposition of the shift operator. Using kernels of type I and II, we define the stationarity concept and filtering properties on digraphs. We further generalize the concept of Wiener filter and the related optimization framework to digraphs. To validate the concepts, we apply our theories numerically to denoise and recover temperature values in some cities in France based on real recordings that are manually noise contaminated. © 2024 IEEE
  6. Keywords:
  7. Graph Fourier transform ; Graph signal ; Wiener filter ; White noise ; De-Noise ; Filtering properties ; Jordan decomposition ; Optimization framework ; Shift operators ; Stationarity ; Stationary process ; Directed graphs
  8. Source: 2024 12th Iran Workshop on Communication and Information Theory, IWCIT 2024 ; 2024 ; 979-835038709-4 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/10553092