Graph Signal Separation Based on Smoothness or Sparsity in the Frequency Domain

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Mohammadi, Sara | 2022

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55200 (05)
University: Sharif University of Technolog
Department: Electrical Engineering
Advisor(s): Babaiezadeh, Massoud; Thanou, Dorina
Abstract:
Blind separation of mixed graph signals is one of the new topics in the field of graph signal processing. However, similar to the most proposed methods for separating traditional signals, it is assumed that the number of observed signals is equal to or greater than the number of sources. In this thesis, we show that a signal can be uniquely decomposed into the summation of a set of smooth graph signals, up to the indeterminacy of their DC values. From the blind source separation point of view, this is like the separation of a set of graph signals from a single mixture, contrary to traditional blind source separation in which at least two observed mixtures are required. Moreover, we generalize the approach to a wider family of signals, which are not necessarily smooth, but exhibit some sparse frequency characteristics in the graph Fourier domain. Furthermore, we state a sufficient condition for recoverability of the graph signals in a special case. Numerical simulations confirm the good performance of our approach in separating a mixture of graph signals.
Keywords:
Graph Signal Processing ; Blind Sources Separation (BSS) ; Smooth Graph Signal ; Multi-Layer Graphs ; Graph Signal Separation (GSS) ; Frequency Domain