CSIAM Transactions on Applied Mathematics最新文献_第5页

Combined Second and Fourth-Order PDEs Model and Associated Variational Problems for Geometric Images Inpainting and Denoising 几何图像的二阶和四阶组合偏微分方程模型及其相关的变分问题修复和去噪

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2021-06-01 DOI: 10.4208/csiam-am.so-2020-0007

A. Theljani

引用次数: 0

A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction 多通道/模态图像重构的一般非lipschitz联合正则化模型

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2021-06-01 DOI: 10.4208/csiam-am.2020-0029

Yiming Gao & ChunlinWu

{"title":"A General Non-Lipschitz Joint Regularized Model for Multi-Channel/Modality Image Reconstruction","authors":"Yiming Gao & ChunlinWu","doi":"10.4208/csiam-am.2020-0029","DOIUrl":"https://doi.org/10.4208/csiam-am.2020-0029","url":null,"abstract":". Multi-channel/modality image joint reconstruction has gained much re-search interest in recent years. In this paper, we propose to use a nonconvex and non-Lipschitz joint regularizer in a general variational model for joint reconstruction un-der additive measurement noise. This framework has good ability in edge-preserving by sharing common edge features of individual images. We study the lower bound theory for the non-Lipschitz joint reconstruction model in two important cases with Gaussian and impulsive measurement noise, respectively. In addition, we extend pre-vious works to propose an inexact iterative support shrinking algorithm with prox-imal linearization for multi-channel image reconstruction (InISSAPL-MC) and prove that the iterative sequence converges globally to a critical point of the original objective function. In a special case of single channel image restoration, the convergence result improves those in the literature. For numerical implementation, we adopt primal dual method to the inner subproblem. Numerical experiments in color image restoration and two-modality undersampled magnetic resonance imaging (MRI) reconstruction show that the proposed non-Lipschitz joint reconstruction method achieves consider-able improvements in terms of edge preservation for piecewise constant images com-pared to existing methods.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42485514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Multi-Layer Hierarchical Structures 多层分层结构

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2021-06-01 DOI: 10.4208/CSIAM-AM.2021.NLA.02

J. Xia

{"title":"Multi-Layer Hierarchical Structures","authors":"J. Xia","doi":"10.4208/CSIAM-AM.2021.NLA.02","DOIUrl":"https://doi.org/10.4208/CSIAM-AM.2021.NLA.02","url":null,"abstract":"In structured matrix computations, existing rank structures such as hierarchically semiseparable (HSS) forms admit fast and stable factorizations. However, for discretized problems, such forms are restricted to 1D cases. In this work, we propose a framework to break such a 1D barrier. We study the feasibility of designing multilayer hierarchically semiseparable (MHS) structures for the approximation of dense matrices arising from multi-dimensional discretized problems such as certain integral operators. The MHS framework extends HSS forms to higher dimensions via the integration of multiple layers of structures, i.e., structures within the dense generator representations of HSS forms. Specifically, in the 2D case, we lay theoretical foundations and justify the existence of MHS structures based on the fast multipole method (FMM) and algebraic techniques such as representative subset selection. Rigorous numerical rank bounds and conditions for the structures are given. Representative subsets of points and a multi-layer tree are used to intuitively illustrate the structures. The MHS framework makes it convenient to explore multidimensional FMM structures. MHS representations are suitable for stable direct factorizations and can take advantage of existing methods and analysis well developed for simple HSS methods. Numerical tests for some discretized operators show that the appropriate inner-layer numerical ranks are significantly smaller than the off-diagonal numerical ranks used in standard HSS approximations. AMS subject classifications: 15A23, 65F05, 65F30","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47425223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Distributed-Memory $mathscr{H}$-Matrix Algebra I: Data Distribution and Matrix-Vector Multiplication $mathscr{H}$-矩阵代数I:数据分布和矩阵向量乘法

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2021-06-01 DOI: 10.4208/csiam-am.2020-0206

Yingzhou Li, J. Poulson, Lexing Ying

引用次数: 0

Existence, Uniqueness and Energy Scaling of (2+1)-Dimensional Continuum Model for Stepped Epitaxial Surfaces with Elastic Effects 具有弹性效应的台阶外延表面（2+1）维连续体模型的存在性、唯一性和能量标度

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2021-03-16 DOI: 10.4208/csiam-am.so-2022-0024

Gang-Han Fan, T. Luo, Y. Xiang

{"title":"Existence, Uniqueness and Energy Scaling of (2+1)-Dimensional Continuum Model for Stepped Epitaxial Surfaces with Elastic Effects","authors":"Gang-Han Fan, T. Luo, Y. Xiang","doi":"10.4208/csiam-am.so-2022-0024","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0024","url":null,"abstract":"We study the 2+1 dimensional continuum model for the evolution of stepped epitaxial surface under long-range elastic interaction proposed by Xu and Xiang (SIAM J. Appl. Math. 69, 1393-1414, 2009). The long-range interaction term and the two length scales in this model makes PDE analysis challenging. Moreover, unlike in the 1+1 dimensional case, there is a nonconvexity contribution in the total energy in the 2+1 dimensional case, and it is not easy to prove that the solution is always in the well-posed regime during the evolution. In this paper, we propose a modified 2+1 dimensional continuum model based on the underlying physics. This modification fixes the problem of possible illposedness due to the nonconvexity of the energy functional. We prove the existence and uniqueness of both the static and dynamic solutions and derive a minimum energy scaling law for them. We show that the minimum energy surface profile is mainly attained by surfaces with step meandering instability. This is essentially different from the energy scaling law for the 1+1 dimensional epitaxial surfaces under elastic effects attained by step bunching surface profiles. We also discuss the transition from the step bunching instability to the step meandering instability in 2+1 dimensions.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46718709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold Stiefel流形优化问题的乘子校正方法

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-11-30 DOI: 10.4208/csiam-am.SO-2020-0008

Lei Wang, Bin Gao, Xin Liu

引用次数: 12

Optimization with Least Constraint Violation 具有最小约束违反的优化

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-10-06 DOI: 10.4208/csiam-am.2020-0043

Yuhong Dai, Liwei Zhang

{"title":"Optimization with Least Constraint Violation","authors":"Yuhong Dai, Liwei Zhang","doi":"10.4208/csiam-am.2020-0043","DOIUrl":"https://doi.org/10.4208/csiam-am.2020-0043","url":null,"abstract":"Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing with these problems is to extend the constrained optimization problem as the one optimizing the objective function over the set of points with the least constraint violation. Firstly, the minimization problem with least constraint violation is proved to be an Lipschitz equality constrained optimization problem when the original problem is a convex optimization problem with possible inconsistent conic constraints, and it can be reformulated as an MPEC problem. Secondly, for nonlinear programming problems with possible inconsistent constraints, various types of stationary points are presented for the MPCC problem which is equivalent to the minimization problem with least constraint violation, and an elegant necessary optimality condition, named as L-stationary condition, is established from the classical optimality theory of Lipschitz continuous optimization. Finally, the smoothing Fischer-Burmeister function method for nonlinear programming case is constructed for solving the problem minimizing the objective function with the least constraint violation. It is demonstrated that, when the positive smoothing parameter approaches to zero, any point in the outer limit of the KKT-point mapping is an L-stationary point of the equivalent MPCC problem.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48541755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Symmetry-Consistent Expansion of Interaction Kernels Between Rigid Molecules 刚性分子间相互作用核的对称一致展开

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-17 DOI: 10.4208/csiam-am.SO-2021-0034

Jie Xu

引用次数: 5

An Adaptive Data-Fitting Model for Speckle Reduction of Log-Compressed Ultrasound Images 对数压缩超声图像去斑点的自适应数据拟合模型

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0010

Yiming Gao

引用次数: 0

An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations 球面约束二次优化中向量2-范数的隐式评价方法