Joint Time-Vertex Fractional Fourier Transform

📅 2022-03-15
🏛️ Signal Processing
📈 Citations: 6
Influential: 0
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🤖 AI Summary
To address the challenge of jointly modeling time-structure coupling dynamics in time-varying graph signals—i.e., vertex-located continuous-time series—within non-Euclidean domains, this paper proposes the Joint Vertex-Time Fractional Fourier Transform (JVF-TFT). For the first time, the fractional Fourier transform is extended to the joint vertex-time domain via the tensor product of the graph Fourier transform and the classical fractional Fourier transform, yielding a tunable-order parametric joint spectral representation. This framework enables sparse representation and localized analysis of non-stationary, non-Euclidean signals while achieving joint spectral energy concentration. Experiments on traffic flow and electroencephalography (EEG) data demonstrate that JVF-TFT significantly outperforms conventional decoupled-domain methods in signal reconstruction accuracy, noise robustness, compression ratio, and discriminative performance.
Problem

Research questions and friction points this paper is trying to address.

Extends Fourier transform to fractional orders.
Enables joint time-vertex signal processing.
Improves denoising and clustering performance.
Innovation

Methods, ideas, or system contributions that make the work stand out.

Joint Time-Vertex Fractional Fourier Transform
Fractional analysis for time-vertex signals
Tikhonov regularization-based denoising
T
Tuna Alikaşifoğlu
Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Türkiye; UM RAM, Bilkent University, Ankara, Türkiye
B
Bunyamin Kartal
WINS Lab, Massachusetts Institute of Technology (MIT), Cambridge, MA, USA
E
Eray Özgünay
Politecnico di Milano, Milano, Italy
A
Aykut Koç
Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Türkiye; UM RAM, Bilkent University, Ankara, Türkiye