IEEE Transactions on Signal Processing最新文献

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A Distributed Adaptive Algorithm for Non-Smooth Spatial Filtering Problems in Wireless Sensor Networks 无线传感器网络非平滑空间过滤问题的分布式自适应算法
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-10-04 DOI: 10.1109/TSP.2024.3474168
Charles Hovine;Alexander Bertrand
{"title":"A Distributed Adaptive Algorithm for Non-Smooth Spatial Filtering Problems in Wireless Sensor Networks","authors":"Charles Hovine;Alexander Bertrand","doi":"10.1109/TSP.2024.3474168","DOIUrl":"10.1109/TSP.2024.3474168","url":null,"abstract":"A wireless sensor network often relies on a fusion center to process the data collected by each of its sensing nodes. Such an approach relies on the continuous transmission of raw data to the fusion center, which typically has a major impact on the sensors’ battery life. To address this issue in the particular context of spatial filtering and signal fusion problems, we recently proposed the Distributed Adaptive Signal Fusion (DASF) algorithm, which distributively computes a spatial filter expressed as the solution of a smooth optimization problem involving the network-wide sensor signal statistics. In this work, we show that the DASF algorithm can be extended to compute the filters associated with a certain class of non-smooth optimization problems. This extension makes the addition of sparsity-inducing norms to the problem's cost function possible, allowing sensor selection to be performed in a distributed fashion, alongside the filtering task of interest, thereby further reducing the network's energy consumption. We provide a description of the algorithm, prove its convergence, and validate its performance and solution tracking capabilities with numerical experiments.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4682-4697"},"PeriodicalIF":4.6,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142377369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Event-Triggered Multi-Sensor Scheduling for Remote State Estimation Over Packet-Dropping Networks 通过丢包网络进行远程状态估计的事件触发式多传感器调度
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-10-04 DOI: 10.1109/TSP.2024.3473988
Yuxing Zhong;Lingying Huang;Yilin Mo;Dawei Shi;Ling Shi
{"title":"Event-Triggered Multi-Sensor Scheduling for Remote State Estimation Over Packet-Dropping Networks","authors":"Yuxing Zhong;Lingying Huang;Yilin Mo;Dawei Shi;Ling Shi","doi":"10.1109/TSP.2024.3473988","DOIUrl":"10.1109/TSP.2024.3473988","url":null,"abstract":"We study the multi-sensor remote state estimation problem over packet-dropping networks and employ a stochastic event-triggered scheduler to conserve energy and bandwidth. Due to packet drops, the Gaussian property of the system state, commonly used in the literature, no longer holds. We prove that the state instead follows a Gaussian mixture (GM) model and develop the corresponding (optimal) minimum mean-squared error (MMSE) estimator. To tackle the exponential complexity of the optimal estimator, the optimal Gaussian approximate (OGA) estimator and its heuristic GM extension are further derived. Our simulations show that the approximate estimators perform similarly to the optimal estimator with significantly reduced computation time. Furthermore, our proposed scheduler outperforms standard event-triggered schedulers in a target-tracking scenario.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5036-5047"},"PeriodicalIF":4.6,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142377405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Overview of Multi-Object Estimation via Labeled Random Finite Set 通过标记随机有限集进行多目标估计概述
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-10-03 DOI: 10.1109/TSP.2024.3472068
Ba-Ngu Vo;Ba-Tuong Vo;Tran Thien Dat Nguyen;Changbeom Shim
{"title":"An Overview of Multi-Object Estimation via Labeled Random Finite Set","authors":"Ba-Ngu Vo;Ba-Tuong Vo;Tran Thien Dat Nguyen;Changbeom Shim","doi":"10.1109/TSP.2024.3472068","DOIUrl":"10.1109/TSP.2024.3472068","url":null,"abstract":"This article presents the Labeled Random Finite Set (LRFS) framework for multi-object systems–systems in which the number of objects and their states are unknown and vary randomly with time. In particular, we focus on state and trajectory estimation via a multi-object State Space Model (SSM) that admits principled tractable multi-object tracking filters/smoothers. Unlike the single-object counterpart, a time sequence of states does not necessarily represent the trajectory of a multi-object system. The LRFS formulation enables a time sequence of multi-object states to represent the multi-object trajectory that accommodates trajectory crossings and fragmentations. We present the basics of LRFS, covering a suite of commonly used models and mathematical apparatus (including the latest results not published elsewhere). Building on this, we outline the fundamentals of multi-object state space modeling and estimation using LRFS, which formally address object identities/trajectories, ancestries for spawning objects, and characterization of the uncertainty on the ensemble of objects (and their trajectories). Numerical solutions to multi-object SSM problems are inherently far more challenging than those in standard SSM. To bridge the gap between theory and practice, we discuss state-of-the-art implementations that address key computational bottlenecks in the number of objects, measurements, sensors, and scans.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4888-4917"},"PeriodicalIF":4.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10704579","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Framework for Compressed Weighted Nonnegative Matrix Factorization 压缩加权非负矩阵因式分解框架
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-10-01 DOI: 10.1109/TSP.2024.3469830
Farouk Yahaya;Matthieu Puigt;Gilles Delmaire;Gilles Roussel
{"title":"A Framework for Compressed Weighted Nonnegative Matrix Factorization","authors":"Farouk Yahaya;Matthieu Puigt;Gilles Delmaire;Gilles Roussel","doi":"10.1109/TSP.2024.3469830","DOIUrl":"10.1109/TSP.2024.3469830","url":null,"abstract":"In this paper we propose a novel framework that successfully combines random projection or compression to weighted Nonnegative Matrix Factorization (NMF). Indeed a large body of NMF research has focused on the unweighted case—\u0000<italic>i.e.,</i>\u0000 a complete data matrix to factorize—with a few extensions to handle incomplete data. Also most of these works are typically not efficient enough when the size of the data is arbitrarily large. Random projections belong to the major techniques used to process big data and although have been successfully applied to NMF, there was no investigation with weighted NMF. For this reason we propose to combine random projection with weighted NMF, where the weight models the confidence in the data (or the absence of confidence in the case of missing data). We experimentally show the proposed framework to significantly speed-up state-of-the-art NMF methods under some mild conditions when applied on various data.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4798-4811"},"PeriodicalIF":4.6,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142362827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simpler Gradient Methods for Blind Super-Resolution With Lower Iteration Complexity 迭代复杂度更低的盲超分辨率梯度方法
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-30 DOI: 10.1109/TSP.2024.3470071
Jinsheng Li;Wei Cui;Xu Zhang
{"title":"Simpler Gradient Methods for Blind Super-Resolution With Lower Iteration Complexity","authors":"Jinsheng Li;Wei Cui;Xu Zhang","doi":"10.1109/TSP.2024.3470071","DOIUrl":"10.1109/TSP.2024.3470071","url":null,"abstract":"We study the problem of blind super-resolution, which can be formulated as a low-rank matrix recovery problem via vectorized Hankel lift (VHL). The previous gradient descent method based on VHL named PGD-VHL relies on additional regularization such as the projection and balancing penalty, exhibiting a suboptimal iteration complexity. In this paper, we propose a simpler unconstrained optimization problem without the above two types of regularization and develop two new and provable gradient methods named VGD-VHL and ScalGD-VHL. A novel and sharp analysis is provided for the theoretical guarantees of our algorithms, which demonstrates that our methods offer lower iteration complexity than PGD-VHL. In addition, ScalGD-VHL has the lowest iteration complexity while being independent of the condition number. Furthermore, our novel analysis reveals that the blind super-resolution problem is less incoherence-demanding, thereby eliminating the necessity for incoherent projections to achieve linear convergence. Empirical results illustrate that our methods exhibit superior computational efficiency while achieving comparable recovery performance to prior arts.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5123-5139"},"PeriodicalIF":4.6,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sub-Nyquist USF Spectral Estimation: $K$ Frequencies With $6K+4$ Modulo Samples 次奈奎斯特 USF 频谱估计:K 频率与 6K + 4 模数采样
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-30 DOI: 10.1109/TSP.2024.3469068
Ruiming Guo;Yuliang Zhu;Ayush Bhandari
{"title":"Sub-Nyquist USF Spectral Estimation: $K$ Frequencies With $6K+4$ Modulo Samples","authors":"Ruiming Guo;Yuliang Zhu;Ayush Bhandari","doi":"10.1109/TSP.2024.3469068","DOIUrl":"10.1109/TSP.2024.3469068","url":null,"abstract":"Digital acquisition of high bandwidth signxals is particularly challenging when Nyquist rate sampling is impractical. This has led to extensive research in sub-Nyquist sampling methods, primarily for spectral and sinusoidal frequency estimation. However, these methods struggle with high-dynamic-range (HDR) signals that can saturate analog-to-digital converters (ADCs). Addressing this, we introduce a novel sub-Nyquist spectral estimation method, driven by the Unlimited Sensing Framework (USF), utilizing a multi-channel system. The sub-Nyquist USF method aliases samples in both amplitude and frequency domains, rendering the inverse problem particularly challenging. Towards this goal, our exact recovery theorem establishes that \u0000<inline-formula><tex-math>$K$</tex-math></inline-formula>\u0000 sinusoids of arbitrary amplitudes and frequencies can be recovered from \u0000<inline-formula><tex-math>$6K+4$</tex-math></inline-formula>\u0000 modulo samples, remarkably, independent of the sampling rate or folding threshold. In the true spirit of sub-Nyquist sampling, via modulo ADC hardware experiments, we demonstrate successful spectrum estimation of HDR signals in the kHz range using Hz range sampling rates (0.078% Nyquist rate). Our experiments also reveal up to a 33-fold improvement in frequency estimation accuracy using one less bit compared to conventional ADCs. These findings open new avenues in spectral estimation applications, e.g., radars, direction-of-arrival (DoA) estimation, and cognitive radio, showcasing the potential of USF.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5065-5076"},"PeriodicalIF":4.6,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Waveform Design for MIMO DFRC Systems: Finer Sensing and Safer Communications MIMO DFRC 系统的波形设计:更精细的传感和更安全的通信
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-30 DOI: 10.1109/TSP.2024.3470219
Da Li;Bo Tang;Lei Xue
{"title":"Waveform Design for MIMO DFRC Systems: Finer Sensing and Safer Communications","authors":"Da Li;Bo Tang;Lei Xue","doi":"10.1109/TSP.2024.3470219","DOIUrl":"10.1109/TSP.2024.3470219","url":null,"abstract":"This paper considers the design of constant-envelope waveforms for multiple-input-multiple-output (MIMO) dual-function radar communication (DFRC) systems. The purpose is to improve the angle estimation performance of the multiple signal classification (MUSIC) algorithm through minimizing its asymptotic estimation error bound. To guarantee the communication performance, we enforce an energy constraint as well as a cosine similarity-based constraint on the synthesized communication signals. Additionally, we constrain the energy transmitted toward each potential eavesdropper to a low level, which prevents the waveforms from being intercepted. To tackle the encountered non-convex optimization problem, we develop two iterative algorithms. The first algorithm is based on the minorization-maximization method, wherein we construct a quadratic surrogate to minorize the approximate objective function. Then we use the alternating direction method of multipliers (ADMM) to tackle the quadratic programming problem. In the second algorithm, we directly tackle the waveform design problem by the ADMM method. Numerical examples are provided to show that through elaborate waveform design, the MIMO DFRC system is capable to realize high-performance target localization and covert communications simultaneously.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4509-4524"},"PeriodicalIF":4.6,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing 优化大规模网络切片的高效本德斯分解法
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-27 DOI: 10.1109/TSP.2024.3469382
Wei-Kun Chen;Zheyu Wu;Rui-Jin Zhang;Ya-Feng Liu;Yu-Hong Dai;Zhi-Quan Luo
{"title":"An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing","authors":"Wei-Kun Chen;Zheyu Wu;Rui-Jin Zhang;Ya-Feng Liu;Yu-Hong Dai;Zhi-Quan Luo","doi":"10.1109/TSP.2024.3469382","DOIUrl":"10.1109/TSP.2024.3469382","url":null,"abstract":"This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4935-4949"},"PeriodicalIF":4.6,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decentralized Learning Based on Gradient Coding With Compressed Communication 基于梯度编码的分散学习与压缩通信
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-26 DOI: 10.1109/TSP.2024.3467262
Chengxi Li;Mikael Skoglund
{"title":"Decentralized Learning Based on Gradient Coding With Compressed Communication","authors":"Chengxi Li;Mikael Skoglund","doi":"10.1109/TSP.2024.3467262","DOIUrl":"10.1109/TSP.2024.3467262","url":null,"abstract":"This paper considers the problem of \u0000<italic>decentralized learning (DEL)</i>\u0000 with stragglers under the communication bottleneck. In the literature, various gradient coding techniques have been proposed for \u0000<italic>distributed learning</i>\u0000 with stragglers by letting the devices transmit encoded gradients based on redundant training data. However, those techniques can not be directly applied to fully decentralized scenarios as considered in this paper due to the lack of a global model in DEL. To overcome this shortcoming, we first propose a new \u0000<underline>go</u>\u0000ssip-based DEL method with gradient \u0000<underline>co</u>\u0000ding (GOCO). In GOCO, to mitigate the negative impact of stragglers, the devices update the parameter vectors with encoded gradients based on stochastic gradient coding before averaging in a gossip-based manner. To further reduce the communication overhead associated with GOCO, we propose an enhanced version of GOCO, namely GOCO with compressed communication (2-GOCO), where the devices transmit compressed messages instead of the raw parameter vectors. The convergence of the proposed methods is analyzed for strongly convex loss functions. Simulation results demonstrate that the proposed methods outperform the baseline methods, which attain better learning performance under the same communication overhead.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4713-4729"},"PeriodicalIF":4.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142325530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint Waveform Design and Antenna Selection for MIMO Radar Beam Scanning 多输入多输出雷达波束扫描的联合波形设计和天线选择
IF 4.6 2区 工程技术
IEEE Transactions on Signal Processing Pub Date : 2024-09-26 DOI: 10.1109/TSP.2024.3468724
Wen Fan;Xuhui Fan;Junli Liang;Hing Cheung So
{"title":"Joint Waveform Design and Antenna Selection for MIMO Radar Beam Scanning","authors":"Wen Fan;Xuhui Fan;Junli Liang;Hing Cheung So","doi":"10.1109/TSP.2024.3468724","DOIUrl":"10.1109/TSP.2024.3468724","url":null,"abstract":"A key task of antenna array is to radiate multiple patterns for beam scanning. While antenna selection can offer additional degrees of freedom in beampattern synthesis. This paper presents a method for antenna selection and beam scanning in a colocated wideband multiple-input multiple-output radar system. Our approach integrates the peak-to-average power ratio (PAPR), energy, and binary constraints, where the last one is employed for antenna selection, in the design. The aim is to match a set of given beampattern masks by jointly determining the antenna positions and a set of probing waveforms, allowing for effective beam scanning. The resultant problem is complex due to the involvement of large-scale, nonconvex, and nonsmooth optimization caused by the PAPR and nonconvex binary constraints, as well as max and modulus operations in the objective function. To address the issues, we start by converting the min-max optimization problem into an iteratively reweighted least squares (IRLS) problem using the Lawson algorithm. Then, we replace the nonsmooth nonconvex objective function with a convex majorization function. Finally, we apply the alternating direction method of multipliers to solve the majorized IRLS problem. Our convergence analysis shows that the proposed algorithms ensure a stationary solution. Additionally, we provide numerical examples to demonstrate the effectiveness of the algorithm.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"4479-4492"},"PeriodicalIF":4.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142325228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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