In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical structure used in fields such as neuroscience, critical infrastructure, and robot coordination, further complicates the issue. Recent results generalized the total variation of a graph signal to that of directed variation as a motivating principle for developing a graphical Fourier transform (GFT). Here, we extend these techniques to concepts of signal variation appropriate for indefinite and complex-valued graphs and use them to define a GFT for these classes of graph. Simulation results on random graphs are presented, as well as a case study of a portion of the fruit fly connectome.
Quantum Integrated Sensing and Computation with Indefinite Causal Order
Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, 5612 AP, The Netherlands（埃因霍温理工大学电气工程系信号处理系统组）
Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs
Neuro-X Institute, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院神经-X研究所）；Department of Radiology and Medical Informatics, University of Geneva（日内瓦大学放射学与医学信息学系）
The Companion Model -- a Canonical Model in Graph Signal Processing
介绍了由$\textit{canonical}$图和$\textit{canonical}$移位定义的$\textit{canonical}$图信号模型、$\textit{companion}$图和$\textit{companion}$移位。这些都是规范的，因为在标准条件下，我们表明，任何图形信号处理（GSP）模型可以转换为规范模型。获得这一点的变换是我们引入的图$z$ -变换（$\textrm{G$ z $T}$）。GSP规范模型最接近离散信号处理（DSP）时间信号模型：伴随移位的结构分解为线移位和信号连续，就像DSP移位一样，并且GSP规范图是具有反映信号连续条件的终端条件的有向线图。我们进一步表明，令人惊讶的是，在规范模型中，卷积的图形信号是快速卷积的DSP FFT。
Statistical Testing on Directed Graphs by Surrogate Data Generation
Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, and the Department of Radiology and Medical Informatics, University of Geneva（Neuro-X研究所，瑞士联邦理工学院洛桑校区，日内瓦大学放射科与医学信息学系）
Dept. of Signal Theory and Communications, Rey Juan Carlos University, Madrid, Spain（信号理论与通信系，雷亚尔·卡洛斯大学，马德里，西班牙）；Dept. of Electrical and Computer Engineering, University of Rochester（电气与计算机工程系，罗切斯特大学）
