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Convolution Type of Metaplectic Cohen's Distribution Time-Frequency Analysis Theory, Method and Technology

IEEE Transactions on Information Theory 2025年第3期71卷 2292-2314页

作者： Cui, Manjun Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng Nanjing University of Information Science and Technology School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing210044 China Nanjing University of Information Science and Technology School of Mathematics and Statistics Nanjing210044 China Shanghai Jiao Tong University Key Laboratory of System Control and Information Processing Ministry of Education Shanghai200240 China Hainan Normal University Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China Nanjing University of Information Science and Technology School of Remote Sensing and Geomatics Engineering Nanjing210044 China

The conventional Cohen's distribution can't meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen's distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen's distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen's distribution filtering method, the adaptive JFMWD-based Cohen's distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen's distribution filtering method in noise suppression. © 1963-2012 IEEE.

关键词： Adaptive filtering

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Dynamic and static Lagrange multiplier μ based Bayesian CP factorization with orthogonal factors: Theory and applications

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Signal Processing 2025年 236卷

作者： Zhou, Jing Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province and Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

The existing μ-Singular Value Decomposition (μ-SVD) denoising algorithm is capable of extracting gear fault information under strong noise conditions. However, this algorithm is only applicable to two-dimensional real-valued data and lacks a mechanism for implementing Automatic Rank Determination (ARD) in high-dimensional data. In this paper, a Bayesian and Tensor treatment of μ-SVD is employed to enable ARD. To further investigate the impact of the Lagrange multiplier μ on the proposed μ-variational Bayesian (μ-VB) algorithm, we examine its performance from both static and dynamic perspectives. Simulation results demonstrate that the μ-VB algorithm achieves ARD and performs well in noise reduction. Further the μ-VB algorithm performs better in wireless communication and linear image coding across numerical domains, tensor sizes, orthogonal factors, and μ settings. © 2025 Elsevier B.V.

关键词： Tensors

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Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

arXiv

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arXiv 2025年

作者： Cui, Manjun Zhang, Zhichao School of Mathematics and Statistics The Center for Applied Mathematics of Jiangsu Province The Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

Graph signal processing (GSP) has emerged as a powerful framework for analyzing data on irregular domains. In recent years, many classical techniques in signal processing (SP) have been successfully extended to GSP. Among them, chirp signals play a crucial role in various SP applications. However, graph chirp signals have not been formally defined despite their importance. Here, we define graph chirp signals and establish a comprehensive theoretical framework for their analysis. We propose the graph fractional vertex-frequency energy distribution (GFED), which provides a powerful tool for processing and analyzing graph chirp signals. We introduce the general fractional graph distribution (GFGD), a generalized vertex-frequency distribution, and the reduced interference GFED, which can suppress cross-term interference and enhance signal clarity. Furthermore, we propose a novel method for detecting graph signals through GFED domain filtering, facilitating robust detection and analysis of graph chirp signals in noisy environments. Moreover, this method can be applied to real-world data for denoising more effective than some state-of-the-arts, further demonstrating its practical significance. Copyright © 2025, The Authors. All rights reserved.

关键词： Wiener filtering

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Multi-Stakeholder Resilient Infrastructure Decision Support under Dynamic Environmental and Adaptive Adversarial Settings

Multi-Stakeholder Resilient Infrastructure Decision Support ...

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2019 IEEE International Symposium on Technologies for Homeland Security, HST 2019

作者： Warner, Mary Chatterjee, Samrat Yadav, Nishant Brigantic, Robert Ganguly, Auroop Civil and Environmental Engineering Northeastern University Boston United States Applied Statistics and Computational Modeling Pacific Northwest National Laboratory Richland United States

ISBN: (纸本)9781728150925

The 2017 U.S. National Security Strategy indicates a need to reduce risk and build resilience against targeted and natural hazards. Simultaneously, these targeted and natural hazards pose a risk beyond the immediate system for which they are impacting due to the interconnectivity of our social, cyber, and infrastructure networks. Each stakeholder-including, but not limited to, policy makers and system operators-have competing and cooperative interests for the ultimate functionality of the individual and overarching system. These multi-criteria and multi-stakeholder problems require a risk assessment and resource allocation tool that is generalizable for multiple stakeholders in order to inform optimal decision making practices in an effort to prepare for any given hazard. This research aims to incorporate resilience alternatives alongside risk assessment metrics using an optimization based decision making framework based upon a multiple-criteria decision making (MCDM) methodology. It will demonstrate a Resilient Infrastructure Decision Support (RIDS) toolset with a top-down decision analysis and bottom-up risk assessment. Through the use of combined simulated and truth-grounded data, infrastructure asset and portfolio-level resource allocation will be determined and multi-stakeholder decision making patterns will be evaluated. Boston Logan Airport and Port Authority will be used as a case study to inform and evaluate the toolset and results can be grounded based upon stakeholder buy-in and historical event inter-comparison. Results intend to be informative to a game theoretical framework. © 2019 IEEE.

关键词： Risk assessment

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Challenges in biomarker discovery: Combining expert insights with statistical analysis of complex omics data

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Expert Opinion on Medical Diagnostics 2013年第1期7卷 37-51页

作者： McDermott, Jason E. Wang, Jing Mitchell, Hugh Webb-Robertson, Bobbie-Jo Hafen, Ryan Ramey, John Rodland, Karin D. Applied Statistics and Computational Modeling Pacific Northwest National Laboratory Computational Biology and Bioinformatics Richland WA 99352 902 Battelle Blvd. United States Biological Sciences for Computational Biology and Bioinformatics Pacific Northwest National Laboratory Computational Biology and Bioinformatics Richland WA 99352 902 Battelle Blvd. United States

Introduction: The advent of high throughput technologies capable of comprehensive analysis of genes, transcripts, proteins and other significant biological molecules has provided an unprecedented opportunity for the identification of molecular markers of disease processes. However, it has simultaneously complicated the problem of extracting meaningful molecular signatures of biological processes from these complex datasets. The process of biomarker discovery and characterization provides opportunities for more sophisticated approaches to integrating purely statistical and expert knowledge-based approaches. Areas covered: In this review we will present examples of current practices for biomarker discovery from complex omic datasets and the challenges that have been encountered in deriving valid and useful signatures of disease. We will then present a high-level review of data-driven (statistical) and knowledge-based methods applied to biomarker discovery, highlighting some current efforts to combine the two distinct approaches. Expert opinion: Effective, reproducible and objective tools for combining data-driven and knowledge-based approaches to identify predictive signatures of disease are key to future success in the biomarker field. We will describe our recommendations for possible approaches to this problem including metrics for the evaluation of biomarkers. © 2013 Informa UK, Ltd.

关键词： Biomarkers Classification Data integration Expert knowledge Molecular signatures

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Multi-dimensional graph linear canonical transform

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Digital Signal Processing 2025年 165卷

作者： Na Li Zhichao Zhang School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province and Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing 210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai 200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou 571158 China

Multi-dimensional (M-D) graph signals represent fundamental data structures in various practical applications, including digital imaging systems, sensor network telemetry, and meteorological observation records. The development of efficient transformation methodologies for processing such M-D graph signals within the linear canonical transform domain continues to present significant challenges. This paper introduces two novel transforms: the two-dimensional graph linear canonical transform based on central discrete dilated Hermite functions (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). These foundational constructs are extended to the multi-dimensional domain, resulting in M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analyses reveal that the M-D CM-CC-CM-GLCT algorithm achieves substantial computational complexity reduction compared to its CDDHFs-based counterpart. Numerical simulations further establish that while maintaining comparable additivity performance, the M-D CM-CC-CM-GLCT exhibits enhanced reversibility characteristics. To validate practical applicability, the proposed M-D GLCT framework is implemented in data compression scenarios. Experimental results demonstrating superior algorithmic efficiency and implementation effectiveness compared to multi-dimensional graph fractional Fourier transform.

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Dissipative Travelling Wave Solution for El Nio Tropic Sea-air Coupled Oscillator

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Chinese Geographical Science 2010年第3期20卷 275-280页

作者： WEN Zhaohui LIN Wantao LIN Yihua MO Jiaqit Institute of Applied Mathematics School of Statistics and Applied Mathematics Anhui University of Finance and Economics Bengbu 233030 China State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong Uinversity Shanghai 200240 China

El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.

关键词： El Nifio-Southem Oscillator model variational iteration sea-air oscillator

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Multi-Stakeholder Resilient Infrastructure Decision Support Under Dynamic Environmental and Adaptive Adversarial Settings

Multi-Stakeholder Resilient Infrastructure Decision Support ...

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IEEE Conference on Technologies for Homeland Security

作者： Mary Warner Samrat Chatterjee Nishant Yadav Robert Brigantic Auroop Ganguly Civil and Environmental Engineering Northeastern University Boston USA Applied Statistics and Computational Modeling Pacific Northwest National Laboratory Richland USA

ISBN: (数字)9781728150925

ISBN: (纸本)9781728150932

关键词： Stakeholders Airports Resilience Portfolios Hazards Risk management Decision making

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Dissipative Travelling Wave Solution for El Nifio Tropic Sea-air Coupled Oscillator

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中国地理科学(英文版) 2010年第3期 275-280页

作者： WEN Zhaohui LIN Wantao LIN Yihua MO Jiaqit Institute of Applied Mathematics School of Statistics and Applied Mathematics Anhui University of Finance and Economics Bengbu China State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Anhui Normal University Wuhu China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong Uinversity Shanghai China

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Decentralized computation of pareto optimal pure nash equilibria of Boolean games with privacy concerns

Decentralized computation of pareto optimal pure nash equili...

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6th International Conference on Agents and Artificial Intelligence, ICAART 2014

作者： De Clercq, Sofie Bauters, Kim Schockaert, Steven Mihaylov, Mihail De Cock, Martine Nowé, Ann Dept. of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium School of Electronics Electrical Engineering and Computer Science Queen's University Belfast United Kingdom School of Computer Science and Informatics Cardiff University Cardiff United Kingdom Computational Modeling Lab Vrije Universiteit Brussel Brussels Belgium

ISBN: (纸本)9789897580161

In Boolean games, agents try to reach a goal formulated as a Boolean formula. These games are attractive because of their compact representations. However, few methods are available to compute the solutions and they are either limited or do not take privacy or communication concerns into account. In this paper we propose the use of an algorithm related to reinforcement learning to address this problem. Our method is decentralized in the sense that agents try to achieve their goals without knowledge of the other agents' goals. We prove that this is a sound method to compute a Pareto optimal pure Nash equilibrium for an interesting class of Boolean games. Experimental results are used to investigate the performance of the algorithm. Copyright © 2014 SCITEPRESS.

关键词： Reinforcement learning

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