Discrete Linear Canonical Transform on Graphs: Fast Sampling Set Selection Method

With the flourishing development of graph signal processing, an increasing number of classical signal processing methods are being incorporated into this field, and the graph linear canonical transform (GLCT) is one such example. In this paper, we address the problem of signal sampling set selection in the GLCT domain based on the proposed GLCT sampling theory. We present a novel fast sampling method. Furthermore, we discuss the relationship between the proposed method and existing sampling set selection methods based on the GLCT spectrum. It is demonstrated that the proposed method considers GLCT spectrum information without the need for the eigendecomposition of the variation operator. Finally, the performance of the proposed method was validated through the selection of vertices, comparing results in terms of reconstruction error and recovery time, which demonstrated its superior efficacy.