Kernel-based Sampling of Graph Signals via Graph Sampling Expansion Theorem

Sampling expansion theorem (SET) plays an important role in discrete signal processing (DSP) for recovering bandlimited signals, while its counterpart in graph signal processing (GSP) has not been thoroughly investigated. In this paper, we will propose one graph SET (gSET) for signals lived in kernel space and then derive one fast sampling algorithm. Specifically, we at first define gSET using kernel-based reconstruction of graph signals lived in reproducing kernel Hilber space (RKHS). We then utilize the defined gSET of bandlimited graph signals as special case with ideal low-pass kernel to combine the proposed gSET in GSP with SET in DSP. Finally, based on the proposed gSET, we will derive one fast graph sampling scheme to select sample with minimal coverage energy. Experiments on realworld temperature graph data will validate the superiority of the proposed sampling method.