Extracting the power lines and pylons automatically and accurately from airborne LiDAR data is a critical step in inspecting the routine power line, especially in the remote mountainous areas. However, challenges arise in using existing methods to extract the targets from large scenarios of remote mountainous areas since the terrain is undulating, and the features are difficult to distinguish. In this article, to overcome these challenges, we propose a graph convolutional network (GCN)-based method to extract power lines and pylons from Airborne LiDAR point clouds. First, data augmentation and near-ground filtering methods are developed to overcome the problems of insufficient and imbalanced samples in the LiDAR data. Then, a GCN-based framework is proposed to extract the power lines and pylons, which consist of two main modules, i.e., the neighborhood dimension information (NDI) module and the neighborhood geometry information aggregation (NGIA) module. These two modules are designed to strengthen the model’s ability to portray local geometric details. Besides, an attention fusion module is investigated to further improve the NDI and NGIA features. Finally, a line structure constraint algorithm is proposed to identify individual power lines, where the power corridor is reconstructed using a polynomial-based algorithm. Numerical experiments are conducted based on two different power line scenarios acquired in mountainous areas. The results demonstrate the superior performances of the proposed method over several existing algorithms, where the $F_{1}$ score and quality of the power line are 99.3% and 98.6%, and the results of the pylon are 96% and 92.4%, respectively. The identification rate of power line identification is above 98%.

While frequency-domain algorithms have been demonstrated to be powerful for conventional nonlinear signal processing, there is still not much progress in literature dedicated to nonlinear graph signal processing in frequency domain. The difficulties come from the irregular structure of graph signals and the lack of a straightforward description for the nonlinear relationship between input and output graph signals. In this paper, a distributed nonlinear polynomial graph filter (NPGF) is proposed to characterize the nonlinear input-output relationship by employing polynomial-type nonlinearity based on Hadamard product. Then, the nonlinear output graph signal is reformulated based on the multi-dimensional inverse graph Fourier transform (GFT), where the m-dimensional GFT coefficients are defined as explicit functions of input graph spectrum and filter structural factors (filter parameters, graph shift matrix, nonlinear degree, and graph shift order). The effects of filter structural factors on the output graph spectrum are further evaluated by proposing graph frequency response (GFR) coefficients, which inherently characterize the irregular structural behaviors of a distributed NPGF in frequency domain. The nonlinear output graph spectrum is then developed based on GFR vectors by mapping the GFR coefficients in the tensor formulation to the output GFT coefficients in the vector expression. This can greatly improve the efficiency in calculating the output graph signal if the input signal only involves a few frequency components. Finally, algorithms are proposed to design the filter parameters for the desired output signal. Numerical studies are presented to illustrate and validate the proposed frequency-domain framework for nonlinear graph signal processing.

The conventional device authentication of wireless networks usually relies on a security server and centralized process, leading to long latency and risk of single-point of failure. While these challenges might be mitigated by collaborative authentication schemes, their performance remains limited by the rigidity of data collection and aggregated result. They also tend to ignore attacker localization in the collaborative authentication process. To overcome these challenges, a novel collaborative authentication scheme is proposed, where multiple edge devices act as cooperative peers to assist the service provider in distributively authenticating its users by estimating their received signal strength indicator (RSSI) and mobility trajectory (TRA). More explicitly, a distributed learning-based collaborative authentication algorithm is conceived, where the cooperative peers update their authentication models locally, thus the network congestion and response time remain low. Moreover, a situation-aware secure group update algorithm is proposed for autonomously refreshing the set of cooperative peers in the dynamic environment. We also develop an algorithm for localizing a malicious user by the cooperative peers once it is identified. The simulation results demonstrate that the proposed scheme is eminently suitable for both indoor and outdoor communication scenarios, and outperforms some existing benchmark schemes.

Vertex-domain and temporal-domain smoothness of time-varying graph signals are cardinal properties that can be exploited for effective graph signal reconstruction from limited samples. However, existing approaches are not directly applicable when the signal's frequency occupancy changes with time. Moreover, while e.g., sensor network applications can benefit from directed graph models, the non-orthogonality of the graph eigenvectors can challenge spectral-based signal reconstruction algorithms. In this context, here we consider $K$ -sparse time-varying signals with unknown frequency supports. By exploiting the smoothness of the varying graph frequency supports and employing shift operations over directed graphs, we study joint sampling of multiple varying signals based on Schur decomposition to reconstruct each signal by orthogonal frequency components. Firstly, joint frequency support of the multiple signals is identified by proposing a two-stage Individual-Joint sampling scheme. Based on the estimated frequency support, the GFT coefficients of each signal can be recovered using data collected in individual sampling stage. Greedy algorithms are proposed for vertex set selection and graph shift order selection, which enable a robust signal reconstruction against additive noise. Considering the signals in applications may be approximately $K$ -sparse, we further exploit the samples in both individual and joint sampling stages and investigate the optimal signal reconstruction as a convex optimization problem with adaptive frequency support selection. The proposed optimal sampling and reconstruction algorithms outperform several existing schemes in random network and sensor network data gathering.

Processing of signals with irregular structures is a fundamental challenge to the conventional signal processing theories and tools due to the complex structures. Since most of the relationships among such data from engineering applications are inherently nonlinear, those tools which do not take the nonlinearity into account may have limitations in dealing with such relationships. In this paper, a novel nonlinear polynomial graph filter (NPGF) is proposed to facilitate the nonlinear processing of signals with irregular structures. First of all, the nonlinear relationship between the input and output graph signals is built based on Taylor series expansion, which is further developed to utilize the structure information of the irregular structures (i.e., the graph shift S). Specifically, the nonlinear kernels and the nonlinear input terms of the developed nonlinear relationship are both designed to be polynomials of the graph shift S. Such nonlinear polynomial relationship is then defined as the NPGF. The conditions of modeling the input-output relationship on a graph as a NPGF is demonstrated. Note that shift invariance is a fundamental property in signal processing but is not straightforward in the existing nonlinear graph signal processing techniques. Due to the special expression of the NPGF, the shift-invariance is extended to our NPGF, which can conveniently facilitate the analysis and design of graph signals using NPGF and is one of the most important contributions in this paper. Numerical studies that characterize the nonlinear temperature distribution and GDP prediction based on real datasets are presented. Compared with other existing techniques, our NPGF achieves superior capability in characterizing the nonlinear relationship between the input and output graph signals, especially when only very few graph signals can be observed.