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Graph Signal Separation Based on Smoothness or Sparsity in the Frequency Domain
, M.Sc. Thesis Sharif University of Technology ; Babaiezadeh, Massoud (Supervisor) ; Thanou, Dorina (Co-Supervisor)
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...
Graph Signal Separation Based on Smoothness or Sparsity in the Frequency Domain
, Article IEEE Transactions on Signal and Information Processing over Networks ; Volume 9 , 2023 , Pages 152-161 ; 2373776X (ISSN) ; Babaiezadeh, M ; Thanou, D ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2023
Abstract
In this paper, we study the problem of demixing an observed signal, which is the summation of a set of signals that live on a multi-layer graph, by proposing several methods to decompose the observed signal into structured components. For this purpose, we build on two of the most widely-used graph signal models' assumptions, namely smoothness and sparsity in the graph spectral domain. We firstly show that a vector can be uniquely decomposed as the summation of a set of smooth graph signals, up to the indeterminacy of their DC values. So, if the original signals are known to be smooth, it is expected that with such a decomposition all of the original signals are retrieved. From the blind...