Identifying influential nodes in complex networks has developed into a prominent research focus. Classical centrality measures such as degree centrality (DC), betweenness centrality (BC), and K-shell (KS) are increasingly being supplemented or replaced by more effective gravity-based alternatives such as gravity centrality (GC), KS based on GC (KSGC), and GGC. However, existing gravity-based methods further enhance node quality based on single attributes, often neglecting the crucial role of edges as communication channels for information dissemination in unweighted networks. A neighborhood potential-edge-weight gravity centrality (NPGC) considering both the degree of node and the information interaction capability of its neighbors for identifying key nodes is proposed. The potential edge weights, which represent the strength of information interaction between nodes, are defined to capture neighborhood information. The simulation of SIR model is employed on nine real-world unweighted and undirected datasets to assess the efficiency of NPGC. Experimental results show that, compared with eight existing methods, the proposed method has high accuracy and good differentiation.

Three-dimensional target reconstruction from synthetic aperture radar (SAR) imagery is crucial for interpreting complex scattering information in SAR data. However, the intricate electromagnetic scattering mechanisms inherent to SAR imaging pose significant reconstruction challenges. Inspired by the remarkable success of 3D Gaussian Splatting (3D-GS) in optical domain reconstruction, this paper presents a novel SAR Differentiable Gaussian Splatting Rasterizer (SDGR), specifically designed for SAR target reconstruction. Our approach combines Gaussian splatting with the Mapping and Projection Algorithm to compute scattering intensities of Gaussian primitives and generate simulated SAR images through SDGR. Subsequently, the loss function between the rendered image and the ground truth image is computed to optimize the Gaussian primitive parameters representing the scene, while a custom CUDA gradient flow is employed to replace automatic differentiation for accelerated gradient computation. Through experiments involving the rendering of simplified architectural targets and SAR images of multiple vehicle targets, we validate the imaging rationality of SDGR on simulated SAR imagery. Furthermore, the effectiveness of our method for target reconstruction is demonstrated on both simulated and real-world datasets containing multiple vehicle targets, with quantitative evaluations conducted to assess its reconstruction performance. Experimental results indicate that our approach can effectively reconstruct the geometric structures and scattering properties of targets, thereby providing a novel solution for 3D reconstruction in the field of SAR imaging.

This study presents a novel method for learning terrain scattering model parameters by leveraging massive multi-source Earth observation data, aiming to achieve realistic Synthetic Aperture Radar (SAR) data simulation. By integrating Gaofen-3 and Sentinel-1 SAR data with auxiliary datasets, the scattering characteristics of various terrains were extracted and analyzed with respect to angle, season, and resolution. For forward modeling, the scattering models were compared to identify suitable models and parameters. To address the challenge of multiple solutions in parameter learning, multi-angle scattering characteristics were employed for initial value estimation, supported by a probability density-based loss function. During parameter learning, targeted learning rates were set based on the gradients of the scattering models with respect to the parameters. Extensive evaluations demonstrate that the proposed method reliably estimates scene parameter maps while preserving texture features, with simulated multi-angle SAR data based on these maps showing good radiometric consistency with measured data. This work holds considerable application potential, and integrating it with other multi-source data and neural networks will yield more valuable outcomes in the future.

This study proposes a high-dimensional characterization framework for multi-scale natural objects and surfaces scattering properties. The framework employs massive multisource remote sensing data to effectively extract the polarization scattering properties of different objects at multiple global locations. In this research, scattering models such as the Small Perturbation Method (SPM), Integral Equation Model (IEM), and Vector Radiative Transfer (VRT) were used for precise fitting of scattering properties. Utilizing these fitting results as initial values allows for stable and efficient inversion of the texture parameters of the scene. Based on texture parameters, Synthetic Aperture Radar (SAR) images under multiple observation angles were generated, and the comparison with measurement data demonstrates high R consistency and Pearson correlation.

Recovering the target three-dimensional (3D) information from Synthetic Aperture Radar (SAR) images and then reconstructing have always been a challenging research topic. Inspired by computer graphics and differential geometry theory, this paper proposes a forward and inverse integration method for accurate estimation of 3D geometric parameters. A differentiable ray tracing engine is developed for forward and inverse reconstruction from SAR images, referred to as DRT. The approach derives geometry parameter gradients based on SAR scattering and mapping projection imaging mechanisms. The difference between the reference SAR image and the simulated image as the objective function to generate high-quality 3D geometric parameter recovery. This method solves the non-differentiable problem of visibility in the ray tracing process. The effectiveness of the method is verified through simulation experiments. According to the optimized 3D mesh parameters, SAR images from other observation angles can be generated. Therefore, in addition to recovering target information and reconstruction from SAR images, DRT can also be used for multi-view sample expansion tasks.

Synthetic aperture radar (SAR) images are highly sensitive to observation configurations and exhibit significant variations across different viewing angles, making it challenging to represent and learn their anisotropic features. As a result, deep learning methods often generalize poorly across different view angles. Inspired by the concept of neural radiance field (NeRF), this study combines SAR imaging mechanisms with neural networks to propose a novel NeRF model for SAR image generation. Following the mapping and projection principles, a set of SAR images are modeled implicitly as a function of attenuation coefficients and scattering intensities in the 3-D imaging space through a differentiable rendering equation. SAR-NeRF is then constructed to learn the distribution of attenuation coefficients and scattering intensities of voxels, where the vectorized form of the 3-D voxel SAR rendering equation and the sampling relationship between the 3-D space voxels and the 2-D view ray grids are analytically derived. Through quantitative experiments on various datasets, we thoroughly assess the multiview representation and generalization capabilities of SAR-NeRF. In addition, this article includes few-shot classification performance improvement as a metric for generation performance. The study found that using 12 images per class resulted in an accuracy improvement of nearly 10% for the classification algorithm.

The simulation of high-resolution synthetic aperture radar (SAR) imagery in intricate environments remains a formidable challenge. Advancements in reversible microwave-domain surface scattering models are crucial, potentially revolutionizing the fidelity of SAR simulations and streamlining the extraction of target parameters. Drawing inspiration from computer graphics, this article proposes a novel differentiable ray tracing (DRT) approach for microwave rendering and fast SAR imaging. The rendering model utilizes coherent spatially varying (SV) bidirectional scattering distribution function (CSVBSDF) based on the Kirchhoff approximation (KA) and the small perturbation method (SPM), corresponding to specular and diffuse scattering contributions, respectively. SAR imaging is efficiently executed via a fusion of ray tracing (RT) and rapid mapping projection. The innovative DRT reversible engine enables swift estimation of SAR image parameter gradients for direct CSVBSDF surface scattering parameter optimization. The method’s validity is confirmed through comparative analysis with measured SAR images and other methods, demonstrating marked improvements in SAR simulation fidelity across diverse observational scenarios by learning surface scattering parameters.

Simulation of Synthetic Aperture Radar (SAR) image in complex scenes has always been a challenging research. The key step of the simulation is determining the parameters of the bidirectional scattering distribution function (BSDF). However,the lack of BSDF parameters optimization make it difficult to get a good simulation. In this work, an optimal parameter estimation of BSDF based a differentiable ray-tracing is proposed. In this SAR image simulation engine, ray-tracing mapping and projection algorithm (MPA) can be inversely differentiable and thus gradient estimation of parameters can be quickly obtained from simulated SAR images. Additionally, with the help of robust physical scattering model based on small perturbation method (SPM) for microray tracing, a better BSDF is obtained, which improve the performance of SAR simulation.