Journal of Scientific Computing最新文献

Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery 基于非线性层次矩阵因数分解的张量环逼近法实现多维图像复原

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-16 DOI: 10.1007/s10915-024-02670-7

Wei-Hao Wu, Ting-Zhu Huang, Xi-Le Zhao, Hao Zhang, Zhi-Long Han

{"title":"Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery","authors":"Wei-Hao Wu, Ting-Zhu Huang, Xi-Le Zhao, Hao Zhang, Zhi-Long Han","doi":"10.1007/s10915-024-02670-7","DOIUrl":"https://doi.org/10.1007/s10915-024-02670-7","url":null,"abstract":"Recently, tensor ring (TR) approximation has received increasing attention in multi-dimensional image processing. In TR approximation, the key backbone is the shallow matrix factorizations, which approximate the circular unfolding of the multi-dimensional image. However, the shallow matrix factorization limits the standard TR approximation’s ability to represent images with complex details and textures. To address this limitation, we propose a nonlinear hierarchical matrix factorization-based tensor ring (NHTR) approximation. Specifically, instead of the shallow matrix factorization, we introduce the nonlinear hierarchical matrix factorization in NHTR approximation to approximate circularly (lceil frac{N}{2}rceil )-modes unfoldings of an N-th order tensor. Benefiting from the powerful expressive capability of the nonlinear hierarchical matrix factorization, the proposed NHTR approximation can faithfully capture fine details of the clean image compared to classical tensor ring approximation. Empowered with the proposed NHTR, we build a multi-dimensional image recovery model and establish a theoretical error bound between the recovered image and the clean image based on the proposed model. To solve the highly nonlinear and hierarchical optimization problem, we develop an efficient alternating minimization-based algorithm. Experiments on multispectral images and color videos conclusively demonstrate the superior performance of our method over the compared state-of-the-art methods in multi-dimensional image recovery.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fully Discrete Finite Difference Schemes for the Fractional Korteweg-de Vries Equation 分数科特韦格-德-弗里斯方程的完全离散有限差分方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-14 DOI: 10.1007/s10915-024-02672-5

Mukul Dwivedi, Tanmay Sarkar

引用次数: 0

Curvature-Dependent Elastic Bending Total Variation Model for Image Inpainting with the SAV Algorithm 利用 SAV 算法绘制图像的曲率相关弹性弯曲总变化模型

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-12 DOI: 10.1007/s10915-024-02666-3

Caixia Nan, Zhonghua Qiao, Qian Zhang

引用次数: 0

The Optimal Weights of Non-local Means for Variance Stabilized Noise Removal 方差稳定除噪的非局部均值的最佳权重

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-12 DOI: 10.1007/s10915-024-02668-1

Yu Guo, Caiying Wu, Yuan Zhao, Tao Wang, Guoqing Chen, Qiyu Jin, Yiqiu Dong

{"title":"The Optimal Weights of Non-local Means for Variance Stabilized Noise Removal","authors":"Yu Guo, Caiying Wu, Yuan Zhao, Tao Wang, Guoqing Chen, Qiyu Jin, Yiqiu Dong","doi":"10.1007/s10915-024-02668-1","DOIUrl":"https://doi.org/10.1007/s10915-024-02668-1","url":null,"abstract":"The Non-Local Means (NLM) algorithm is a fundamental denoising technique widely utilized in various domains of image processing. However, further research is essential to gain a comprehensive understanding of its capabilities and limitations. This includes determining the types of noise it can effectively remove, choosing an appropriate kernel, and assessing its convergence behavior. In this study, we optimize the NLM algorithm for all variations of independent and identically distributed (i.i.d.) variance-stabilized noise and conduct a thorough examination of its convergence behavior. We introduce the concept of the optimal oracle NLM, which minimizes the upper bound of pointwise (L_{1}) or (L_{2}) risk. We demonstrate that the optimal oracle weights comprise triangular kernels with point-adaptive bandwidth, contrasting with the commonly used Gaussian kernel, which has a fixed bandwidth. The computable optimal weighted NLM is derived from this oracle filter by replacing the similarity function with an estimator based on the similarity patch. We present theorems demonstrating that both the oracle filter and the computable filter achieve optimal convergence rates under minimal regularity conditions. Finally, we conduct numerical experiments to validate the performance, accuracy, and convergence of (L_{1}) and (L_{2}) risk minimization for NLM. These convergence theorems provide a theoretical foundation for further advancing the study of the NLM algorithm and its practical applications.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring 用于盲彩色图像去模糊的四元数感知低库优先级

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-11 DOI: 10.1007/s10915-024-02671-6

Hao Zhang, Te Qi, Tieyong Zeng

{"title":"Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring","authors":"Hao Zhang, Te Qi, Tieyong Zeng","doi":"10.1007/s10915-024-02671-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02671-6","url":null,"abstract":"Blind image deblurring is a critical and challenging task in the field of imaging science due to its severe ill-posedness. Appropriate prior information and regularizations are normally introduced to alleviate this problem. Inspired by the fact that the matrix representing a natural image is intrinsically low-rank or approximately low-rank, we employ the low-rank matrix approximation (LRMA) approach for tackling blind image deblurring problems with unknown kernels. When applied to color image restoration tasks, making use of the quaternion representation in the hypercomplex domain enables us to better illustrate the inner relationships among color channels and thus more accurately characterize color image structure. Following this idea, we develop a novel model for color image blind deblurring by implementing the quaternion representation to the LRMA method. This proposed model facilitates better results for blur kernel estimation through preserving the sharper color intermediate latent image, which is first implemented for addressing the blind color image deblurring problem. Extensive numerical experiments demonstrate that our proposed quaternion-aware low-rank prior model greatly improves the performance when compared with the conventional low-rank based scheme and outperforms some of the state-of-the-art methods in terms of some criteria and visual quality.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Linearly Implicit Schemes Preserve the Maximum Bound Principle and Energy Dissipation for the Time-fractional Allen–Cahn Equation 线性隐式方案保留时间分数艾伦-卡恩方程的最大边界原则和能量消耗

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-11 DOI: 10.1007/s10915-024-02667-2

Huiling Jiang, Dongdong Hu, Haorong Huang, Hongliang Liu

{"title":"Linearly Implicit Schemes Preserve the Maximum Bound Principle and Energy Dissipation for the Time-fractional Allen–Cahn Equation","authors":"Huiling Jiang, Dongdong Hu, Haorong Huang, Hongliang Liu","doi":"10.1007/s10915-024-02667-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02667-2","url":null,"abstract":"This paper presents two highly efficient numerical schemes for the time-fractional Allen–Cahn equation that preserve the maximum bound principle and energy dissipation in discrete settings. To this end, we utilize a generalized auxiliary variable approach proposed in a recent paper (Ju et al. in SIAM J Numer Anal 60:1905–1931, 2022) to reformulate the governing equation into an equivalent system that follows a modified energy functional and the maximum bound principle at each continuous level. By combining the L1-type formula of the Riemann–Liouville fractional derivative with the Crank–Nicolson method, we construct two novel linearly implicit schemes by introducing the first- and second-order stabilized terms, respectively. These schemes are proved to be energy stable and maximum bound principle preserving on nonuniform time meshes with the help of the discrete orthogonal convolution technique. In addition, we obtain the unique solvability of the proposed schemes without any time-space step ratio. Finally, we report extensive numerical results to verify the correctness of the theoretical analysis and the performance of the proposed schemes in long-time simulations.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An HDG and CG Method for the Indefinite Time-Harmonic Maxwell’s Equations Under Minimal Regularity 最小正则性下的无限时谐麦克斯韦方程的 HDG 和 CG 方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-11 DOI: 10.1007/s10915-024-02643-w

Gang Chen, Peter Monk, Yangwen Zhang

引用次数: 0

Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators 多维分项求和算子的三角形和正四面体正交规则

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-09 DOI: 10.1007/s10915-024-02656-5

Zelalem Arega Worku, Jason E. Hicken, David W. Zingg

{"title":"Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators","authors":"Zelalem Arega Worku, Jason E. Hicken, David W. Zingg","doi":"10.1007/s10915-024-02656-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02656-5","url":null,"abstract":"Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal-( textsf{E}) operators, are attractive for entropy-stable discretizations from an efficiency standpoint. However, there is a limited number of such operators, and those currently in existence often have a relatively high node count for a given polynomial order due to a scarcity of suitable quadrature rules. We present several new symmetric positive-weight quadrature rules on triangles and tetrahedra that are suitable for construction of diagonal-( textsf{E}) SBP operators. For triangles, quadrature rules of degree one through twenty with facet nodes that correspond to the Legendre-Gauss-Lobatto and Legendre-Gauss quadrature rules are derived. For tetrahedra, quadrature rules of degree one through ten are presented along with the corresponding facet quadrature rules. All of the quadrature rules are provided in a supplementary data repository. The quadrature rules are used to construct novel SBP diagonal-( textsf{E}) operators, whose accuracy and maximum time-step restrictions are studied numerically.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A High-Accuracy Mode Solver for Acoustic Scattering by a Periodic Array of Axially Symmetric Obstacles 轴对称障碍物周期性阵列声散射的高精度模式求解器

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-05 DOI: 10.1007/s10915-024-02659-2

Hangya Wang, Wangtao Lu

{"title":"A High-Accuracy Mode Solver for Acoustic Scattering by a Periodic Array of Axially Symmetric Obstacles","authors":"Hangya Wang, Wangtao Lu","doi":"10.1007/s10915-024-02659-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02659-2","url":null,"abstract":"This paper is concerned with guided modes of an acoustic wave propagation problem on a periodic array of axially symmetric obstacles. A guided mode refers to a quasi-periodic eigenfield that propagates along the obstacles but decays exponentially away from them in the absence of incidences. Thus, the problem can be studied in an unbound unit cell due to the quasi-periodicity. We truncate the unit cell onto a cylinder enclosing the interior obstacle in terms of utilizing Rayleigh’s expansion to design an exact condition on the lateral boundary. We derive a new boundary integral equation (BIE) only involving the free-space Green function on the boundary of each homogeneous region within the cylinder. Due to the axial symmetry of the boundaries, each BIE is decoupled via the Fourier transform to curve BIEs and they are discretized with high-accuracy quadratures. With the lateral boundary condition and the side quasi-periodic condition, the discretized BIEs lead to a homogeneous linear system governing the propagation constant of a guided mode at a given frequency. The propagation constant is determined by enforcing that the coefficient matrix is singular. The accuracy of the proposed method is demonstrated by a number of examples even when the obstacles have sharp edges or corners.\u0000","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stabilized Variational Formulations of Chorin-Type and Artificial Compressibility Methods for the Stochastic Stokes–Darcy Equations 用于随机斯托克斯-达西方程的乔林型和人工可压缩性方法的稳定变分公式

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-04 DOI: 10.1007/s10915-024-02663-6

Huangxin Chen, Can Huang, Shuyu Sun, Yahong Xiang

{"title":"Stabilized Variational Formulations of Chorin-Type and Artificial Compressibility Methods for the Stochastic Stokes–Darcy Equations","authors":"Huangxin Chen, Can Huang, Shuyu Sun, Yahong Xiang","doi":"10.1007/s10915-024-02663-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02663-6","url":null,"abstract":"In this paper, we consider two different types of numerical schemes for the nonstationary stochastic Stokes–Darcy equations with multiplicative noise. Firstly, we consider the Chorin-type time-splitting scheme for the Stokes equation in the free fluid region. The Darcy equation and an elliptic equation for the intermediate velocity of free fluid coupled with the interface conditions are solved, and then the velocity and pressure in free fluid region are updated by an elliptic system. Secondly, we further consider the artificial compressibility method (ACM) which separates the fully coupled Stokes–Darcy model into two smaller subphysics problems. The ACM reduces the storage and the computational time at each time step, and allows parallel computing for the decoupled problems. The pressure in free fluid region only needs to be updated at each time step without solving an elliptic system. We utilize the RT(_1)-P(_1) pair finite element space and the interior penalty discontinuous Galerkin (IPDG) scheme based on the BDM(_1)-P(_0) finite element space in the spatial discretizations. Under usual assumptions for the multiplicative noise, we prove that both of the Chorin-type scheme and the ACM are unconditionally stable. We present the error estimates for the time semi-discretization of the Chorin-type scheme. Numerical examples are provided to verify the stability estimates for both of schemes. Moreover, we test the convergence rate for the velocity in time for both of schemes, and the convergence rate for the pressure approximation in time average is also tested.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0