Generalized sampling of graph signals with the prior information based on graph fractional Fourier transform

The graph fractional Fourier transform (GFRFT) has been applied to graph signal processing and has become an important tool in graph signal processing. However, most of the graph signals are usually non-bandlimited in the GFRFT domain. How to efficiently sampling and reconstructing these graph signals is a key challenge in the field of graph signal processing. In this paper, we propose a generalized sampling framework for graph signals based on the prior information in the GFRFT domain. In this framework, sampling and reconstruction can be efficiently implemented. Moreover, the framework is not limited by the bandwidth of the fractional Fourier domain of the graph signal. In this study, we first consider the subspace prior of the graph signal. It allows arbitrary input of the graph signal with or without bandlimited in the GFRFT domain. Then, we propose a generalized sampling framework for graph signals based on smoother prior information associated with GFRFT. When the prior space of the graph signal is unknown, the original graph signal can still be reconstructed. Finally, we compare our method with existing sampling techniques. Several experiments are performed to numerically validate the effectiveness of the proposed sampling framework.