Optimal Sampling and Reconstruction of Graph Signals in the Fractional Fourier Domain

Xiaopeng Cheng, Zhichao Zhang, Yangfan He

Graph signal sampling and reconstruction are commonly formulated in the graph Fourier transform (GFT) domain. However, the reconstruction performance may be limited when practical graph signals are not sufficiently concentrated in the GFT spectrum. To address this issue, this paper proposes a graph signal sampling and reconstruction framework based on the graph fractional Fourier transform (GFRFT) domain. The fractional order is introduced as an adjustable spectral domain parameter, and the optimal order is selected to provide a more suitable representation domain for a given graph signal and sampling model. Under a unified sampling reconstruction formulation, subspace, smoothness, and stochastic priors are incorporated, and both unconstrained and predefined reconstruction mechanisms are considered, leading to several fractional domain sampling and reconstruction methods. Furthermore, the theoretical analysis shows that the optimal GFRFT domain can provide a more suitable low-dimensional spectral representation by improving energy concentration and reducing projection residual. The effects of residual leakage and noise amplification are further considered to explain how this representation advantage is translated into reconstruction error reduction. Experimental results show that, GFRFT domain sampling and reconstruction generally achieve better recovery performance than GFT domain methods.