Joint time-vertex linear canonical transform

The emergence of graph signal processing (GSP) has spurred a deep interest in signals that naturally reside on irregularly structured data kernels, such as those found in social, transportation, and sensor networks. Recently, concepts and applications related to time-varying graph signal analysis have matured, linking temporal signal processing techniques with innovative tools in GSP. In this paper, similar to the extension of the graph fractional Fourier transform to the graph linear canonical transform, we define the joint time-vertex linear canonical transform (JLCT) and its properties. This transformation extends the joint time-vertex Fourier transform (JFT) and fractional Fourier transform (JFRFT), broadening the Fourier analysis in both time and vertex domains into the domain of the linear canonical transform (LCT). This offers an enhanced set of the LCT analysis tools for joint time-vertex processing. Applications of the JLCT in dynamic mesh denoising, clustering, and energy compactness demonstrate that JLCT can enhance regression and learning tasks, and can refine and improve the performance of the JFT and the JFRFT.