Browsing by Subject "Signal processing on graphs"

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    Optimal fractional fourier filtering for graph signals
    (IEEE, 2021-05-19) Öztürk, Cüneyd; Özaktaş, Haldun M.; Gezici, Sinan; Koç, Aykut
    Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.
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    ItemOpen Access
    Wiener filtering in joint time-vertex fractional Fourier domains
    (IEEE, 2024) Alikaşifoğlu, Tuna; Kartal, Bünyamin; Koç, Aykut
    Graph signal processing (GSP) uses network structures to analyze and manipulate interconnected signals. These graph signals can also be time-varying. The established joint time-vertex processing framework and corresponding joint time-vertex Fourier transform provide a basis to endeavor such time-varying graph signals. The optimal Wiener filtering problem has been deliberated within the joint time-vertex framework. However, the ordinary Fourier domain is only sometimes optimal for separating the signal and noise; one can achieve lower error rates in a fractional Fourier domain. In this paper, we solve the optimal Wiener filtering problem in the joint time-vertex fractional Fourier domains. We provide a theoretical analysis and numerical experiments with comprehensive comparisons to existing filtering approaches for time-varying graph signals to demonstrate the advantages of our approach.