Sampling of graph signals with successive aggregations based on graph fractional Fourier transform

Abstract

The sampling defined on the graph nodes is a crucial method for graph signals sampling, especially considering graph structure. The sampling theory of the graph frequency domain for bandlimited graph signals has blossomed in recent years. However, it fails for the graph fractional domain bandlimited signals. In this paper, we first develop the theory of successive aggregations sampling associated with the graph fractional Fourier transform (GFRFT). Then, we propose the optimal node selection scheme in the case of noise. Moreover, we present a general sampling framework and prove that the existing graph signal sampling methods are its special cases. Finally, we explore the sparse reconstruction issue based on the developed successive aggregations sampling. Our proposed sampling method outperforms other sampling schemes in reconstruction error. Several experiments are performed to validate the effectiveness of the proposed sampling method numerically.