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On construction of strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus

Science China Mathematics 2025年第5期68卷 1219-1242页

作者： Bochuan Jiang Yaping Wang Fasheng Sun School of Mathematics and Statistics Beijing Jiaotong UniversityBeijing100044China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of EducationSchool of StatisticsEast China Normal UniversityShanghai200062China Key Laboratory for Applied Statistics of Ministry of Education and School of Mathematics and Statistics Northeast Normal UniversityChangchun130024China

Computer experiments require space-filling designs with good low-dimensional projection *** orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions than ordinary orthogonal *** this paper,we address the problem of constructing strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two *** methods typically rely on regular designs or specific nonregular designs as base orthogonal arrays,limiting the sizes of the final ***,we propose two general methods that are easy to implement and applicable to a wide range of base orthogonal *** methods produce space-filling designs that can accommodate a large number of factors,provide significant flexibility in terms of run sizes,and possess appealing low-dimensional projection ***,these designs are ideal for computer experiments.

关键词： computer experiment difference scheme strong orthogonal array column-orthogonality space-filling property

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On the maximin distance properties of orthogonal designs via the rotation

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Science China Mathematics 2023年第7期66卷 1593-1608页

作者： Yaping Wang Fasheng Sun Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of EducationSchool of StatisticsEast China Normal UniversityShanghai 200062China Key Laboratory for Applied Statistics of Ministry of Education School of Mathematics and StatisticsNortheast Normal UniversityChangchun 130024China

Space-filling designs are widely used in computer *** are frequently evaluated by the orthogonality and distance-related *** orthogonal arrays is an appealing approach to constructing orthogonal space-filling *** important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal *** paper studies the maximin L_(2)-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three *** provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G_(2)-aberration *** infinite families of orthogonal or 3-orthogonal U-type designs,which also perform well under the maximin distance criterion,are obtained and *** are presented to show the effectiveness of the constructed designs for building statistical surrogate models.

关键词： computer experiment Latin hypercube design minimum G_(2)-aberration space-filling design U-type design

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Image Copy-Move Forgery Detection in the Social Media Based on a Prior Density Clustering and the Point Density 6th

Image Copy-Move Forgery Detection in the Social Media Base...

引用

6th International Conference on Security and Privacy in New Computing Environments, SPNCE 2023

作者： Lin, Cong Yang, Hai Huang, Ke Wu, Yufeng Wen, Yamin Deng, Yuqiao Applied Laboratory of Dig Data and Education Statistics School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou510320 China School of Information Guangdong University of Finance and Economics Guangzhou510320 China Guangdong Provincial Key Laboratory of Information Security Technology Sun Yat-sen University Guangzhou51006 China

ISBN: (纸本)9783031736988

Copy-move forgery is one common image manipulation technique. Many images are compressed by the social media, but most of the existing copy-move forgery detection schemes are proposed to deal with the uncompressed version of images. To handle this problem, in this paper, a copy-move forgery detection scheme for social media is proposed based on the point density and a prior density clustering. Firstly, the concept of "point density" is proposed, and it is combined with feature extraction to improve the extraction effect. Secondly, the hierarchical matching is adopted, and the keypoints are grouped according to the pixel value. Thirdly, a prior-based density clustering is proposed, called prior-DBSCAN. In this scheme, the matching pairs are divided into start points and end points for clustering, respectively, and the prior region of each cluster is obtained. Then, the clustering with the new cluster radius is performed. Finally, an iterative localization technique is used to obtain the final localization results. Considering the compression of images during their transmission through the social media, the proposed scheme is made more suitable for real-world scenarios. The experimental results demonstrate that the proposed scheme based on a prior density clustering and the point density, which is better and more robust than the state-of-the-art schemes on publicly available datasets. © ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2025.

关键词： Computer forensics

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Deep generative network for image inpainting with gradient semantics and spatial-smooth attention

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Journal of Visual Communication and Image Representation 2024年 98卷

作者： Sheng, Ziqi Xu, Wenbo Lin, Cong Lu, Wei Ye, Long School of Computer Science and Engineering Guangdong Province Key Laboratory of Information Security Technology Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Guangzhou510006 China Applied Laboratory of Dig Data and Education Statistics School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou510320 China State Key Laboratory of Media Convergence and Communication Communication University of China Beijing100024 China

As a powerful forgery operation in the image content security area, image inpainting based on deep generative networks can yield visually appealing outputs but often produces ambiguous artifacts, especially in boundary and high semantic areas. To address this issue, a novel end-to-end network with gradient semantics and spatial-smooth attention (GS-SSA) is proposed, which combines a gradient learning network and an image inpainting network. The gradient learning network is meant to properly anticipate the gradient semantics in the hole region and get a complete gradient semantic map. The image inpainting network utilizes the complete gradient semantic map to better repair the missing pixels and obtain the final inpainting results. Moreover, spatial-smooth attention is introduced into the image inpainting network, considering both the spatial structural relations and the surrounding information in the hole region. Experimental results on public datasets show the superiority of the proposed method, especially in large-hole region tasks. © 2023 Elsevier Inc.

关键词： Semantics

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Copy-Move Forgery Detection Using Regional Density Center Clustering

SSRN

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SSRN 2024年

作者： Lin, Cong Wu, Yufeng Huang, Ke Yang, Hai Deng, Yuqiao Wen, Yamin Applied Laboratory of Dig Data and Education Statistics School of Statistics and Mathematics Guangdong University of Finance & Economics Guangzhou510320 China School of Information Guangdong University of Finance & Economics Guangzhou510320 China Guangdong Provincial Key Laboratory of Information Security Technology Sun Yat-sen University Guangzhou510006 China

In this paper, a novel copy-move forgery detection scheme is proposed. The proposed scheme is based on Regional Density Center (RDC) clustering and Refined Length Homogeneity Filtering (RLHF) policy. First, to obtain an adequate number of keypoints in smooth or small areas of the image, the proposed scheme employs scale normalization and adjustment of the contrast threshold. Subsequently, a matching algorithm based on gray value grouping is used to match the keypoints. RLHF policy is applied to filter the mismatched pairs. To guarantee a good estimation of the affine transformation, the RDC clustering algorithm is proposed to group the matched pairs. Finally, the correlation coefficients are computed to precisely locate the tampered regions. The proposed copy-move forgery detection scheme based on RDC and RLHF can effectively identify duplicated regions of digital images. It demonstrates the effectively and robustness of the proposed scheme over many state-of-the-art schemes on public datasets. © 2024, The Authors. All rights reserved.

关键词： Clustering algorithms

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Deep Generative Network for Image Inpainting with Gradient Semantics and Spatial-Smooth Attention

SSRN

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SSRN 2023年

作者： Sheng, Ziqi Xu, Wenbo Lin, Cong Lu, Wei School of Computer Science and Engineering Guangdong Province Key Laboratory of Information Security Technology Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Guangzhou510006 China Applied Laboratory of Dig Data and Education Statistics School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou510006 China

As a powerful means of tampering in image content security area, image inpainting based on deep generative networks can yield visually appealing outputs but often produces ambiguous artifacts, particularly in boundary and high semantic areas. To address this issue, a novel end-to-end network with gradient semantics and spatial-smooth attention (GS-SSA) is proposed, which combines a gradient learning network and an image inpainting network. The gradient learning network is meant to properly anticipate the gradient semantics in the hole region and get a complete gradient semantic map. The image inpainting network utilizes the complete gradient semantic map to better repair the missing pixels and obtain the final inpainting results. Moreover, spatial-smooth attention is introduced into the image inpainting network, considering the spatial structural relations and the surrounding information in the hole region respectively. © 2023, The Authors. All rights reserved.

关键词： Semantics

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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-dimensional Graph Linear Canonical Transform

arXiv

引用

arXiv 2024年

作者： Li, Na Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province 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 Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and Technology Nanjing210044 China

Many multi-dimensional (M-D) graph signals appear in the real world, such as digital images, sensor network measurements and temperature records from weather observation stations. It is a key challenge to design a transform method for processing these graph M-D signals in the linear canonical transform domain. This paper proposes the two-dimensional graph linear canonical transform based on the central discrete dilated Hermite function (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). Then, extending 2-D CDDHFs-GLCT and 2-D CM-CC-CM-GLCT to M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of the computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analysis shows that the computational complexity of M-D CM-CC-CM-GLCT algorithm is obviously reduced. Simulation results indicate that M-D CM-CC-CM-GLCT achieves comparable additivity to M-D CDDHFs-GLCT, while M-D CM-CC-CM-GLCT exhibits better reversibility. Finally, M-D GLCT is applied to data compression to show its application advantages. The experimental results reflect the superiority of M-D GLCT in the algorithm design and implementation of data compression. Copyright © 2024, The Authors. All rights reserved.

关键词： Chirp modulation

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Native spaces and generalization of Wu functions

arXiv

引用

arXiv 2023年

作者： Huang, Yixuan Wu, Zongmin Zhu, Shengxin School of Mathematics Beijing Normal University China Laboratory of Mathematics and Complex Systems Ministry of Education China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai China Shanghai Center for Mathematical Sciences Shanghai China School of Big Data and Statistics Anhui University Hefei China Research Center for Mathematics Advanced Institute of Natural Science Beijing Normal University Zhuhai519087 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai519087 China

We prove that the native space of a Wu function is a dense subspace of a Sobolev space. An explicit characterization of the native spaces of Wu functions is given. Three definitions of Wu functions are introduced and proven to be equivalent. Based on these new equivalent definitions and the so called f-form tricks, we can generalize the Wu functions into the even-dimensional spaces R2k, while the original Wu functions are only defined in the odd-dimensional spaces R2k+1. Such functions in even-dimensional spaces are referred to as the ‘missing Wu functions’. Furthermore we can generalize the Wu functions into ‘fractional’-dimensional spaces. We call all these Wu functions the generalized Wu functions. The closed form of the generalized Wu functions are given in terms of hypergeometric functions. Finally we prove that the Wu functions and the missing Wu functions can be written as linear combinations of the generalized Wendland *** Codes 65J05, 33C90, 41A05, 41A30, 41A65, 41A63 Copyright © 2023, The Authors. All rights reserved.

关键词： Sobolev spaces

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A Class of Smoothing-regularization Methods to Mathematical Programs with Vanishing Constraints

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数学进展 2024年第5期53卷 953-973页

作者： HU Qingjie MA Lili CHEN Yu School of Mathematics and Computing Science Guangci Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinGuangci541002P.R.China Center for Applied Mathematics of Guangri(GUET) GuilinGuangri541002P.R.China College of General Education Guangdong University of Science and TechnologyDongguanGuangdong523668P.R.China School of Mathematics and Statistics Guangri Normal UniversityGuilinGuangci541004P.R.China

this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing *** methods include the smoothing-regularization method proposed by Kanzow et ***[***.,2013,55(3):733-767]as a special *** the weaker conditions than the ones that have been used by Kanzow et *** 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization *** also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary ***,numerical experiments are given to show the efficiency of the proposed methods.

关键词： mathematical programs with vanishing constraints smoothing-regularization method VC-MFCQ strong stationary point

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