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Journal of Inverse and Ill-Posed Problems最新文献

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The inverse scattering problem for an inhomogeneous two-layered cavity 非均匀双层腔的逆散射问题
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-03 DOI: 10.1515/jiip-2021-0006
Jianguo Ye, G. Yan
{"title":"The inverse scattering problem for an inhomogeneous two-layered cavity","authors":"Jianguo Ye, G. Yan","doi":"10.1515/jiip-2021-0006","DOIUrl":"https://doi.org/10.1515/jiip-2021-0006","url":null,"abstract":"Abstract In this paper, we consider the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements under the condition that the interior interface has a mixed transmission boundary condition. We focus on the mathematical analysis of recovering the shape of the interior interface by using the linear sampling method, including reconstructing the surface conductivity by the same measurements.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47782757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fast multilevel iteration methods for solving nonlinear ill-posed problems 求解非线性不适定问题的快速多层迭代方法
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-03 DOI: 10.1515/jiip-2022-0059
Suhua Yang, Xingjun Luo, Rong Zhang
{"title":"Fast multilevel iteration methods for solving nonlinear ill-posed problems","authors":"Suhua Yang, Xingjun Luo, Rong Zhang","doi":"10.1515/jiip-2022-0059","DOIUrl":"https://doi.org/10.1515/jiip-2022-0059","url":null,"abstract":"Abstract We propose a multilevel iteration method for the numerical solution of nonlinear ill-posed problems in the Hilbert space by using the Tikhonov regularization method. This leads to fast solutions of the discrete regularization methods for the nonlinear ill-posed equations. An adaptive choice of an a posteriori rule is suggested to choose the stopping index of iteration, and the rates of convergence are also derived. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43670165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Approximate Lipschitz stability for phaseless inverse scattering with background information 具有背景信息的无相逆散射的近似Lipschitz稳定性
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-03 DOI: 10.1515/jiip-2023-0001
V. Sivkin
{"title":"Approximate Lipschitz stability for phaseless inverse scattering with background information","authors":"V. Sivkin","doi":"10.1515/jiip-2023-0001","DOIUrl":"https://doi.org/10.1515/jiip-2023-0001","url":null,"abstract":"Abstract We prove approximate Lipschitz stability for monochromatic phaseless inverse scattering with background information in dimension d ≥ 2 {dgeq 2} . Moreover, these stability estimates are given in terms of non-overdetermined and incomplete data. Related results for reconstruction from phaseless Fourier transforms are also given. Prototypes of these estimates for the phased case were given in [R. G. Novikov, Approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy, J. Inverse Ill-Posed Probl. 21 2013, 6, 813–823].","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"441 - 454"},"PeriodicalIF":1.1,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43379446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Reconstruction of modified transmission eigenvalues using Cauchy data 利用柯西数据重构修正传输特征值
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-04-26 DOI: 10.1515/jiip-2022-0014
Juan Liu, Yanfang Liu, Jiguang Sun
{"title":"Reconstruction of modified transmission eigenvalues using Cauchy data","authors":"Juan Liu, Yanfang Liu, Jiguang Sun","doi":"10.1515/jiip-2022-0014","DOIUrl":"https://doi.org/10.1515/jiip-2022-0014","url":null,"abstract":"Abstract The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 2017, 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy data. We propose a reciprocity gap functional method and show that the MTEs can be determined by solving some linear ill-posed integral equations. Numerical examples for both absorbing and non-absorbing media are presented to validate the effectiveness and robustness of the proposed method.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41828482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Reverse time migration for imaging periodic obstacles with electromagnetic plane wave 电磁平面波周期性障碍物成像的逆时偏移
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-04-07 DOI: 10.48550/arXiv.2304.03597
Lide Cai, Junqing Chen
{"title":"Reverse time migration for imaging periodic obstacles with electromagnetic plane wave","authors":"Lide Cai, Junqing Chen","doi":"10.48550/arXiv.2304.03597","DOIUrl":"https://doi.org/10.48550/arXiv.2304.03597","url":null,"abstract":"Abstract We propose novel reverse time migration (RTM) methods for the imaging of periodic obstacles using only measurements from the lower or upper side of the obstacle arrays at a fixed frequency. We analyze the resolution of the lower side and upper side RTM methods in terms of propagating modes of the Rayleigh expansion, Helmholtz–Kirchhoff equation and the distance of the measurement surface to the obstacle arrays, where the periodic structure leads to novel analysis. We give some numerical experiments to justify the competitive efficiency of our imaging functionals and the robustness against noises. Further, numerical experiments show sharp images especially for the vertical part of the periodic obstacle in the lower-RTM case, which is not shared by results for imaging bounded compactly supported obstacles.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44594680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting 基于agent的新西伯利亚地区COVID-19传播数学模型:可识别性、优化与预测
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-04-04 DOI: 10.1515/jiip-2021-0038
O. Krivorotko, Mariia Sosnovskaia, S. Kabanikhin
{"title":"Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting","authors":"O. Krivorotko, Mariia Sosnovskaia, S. Kabanikhin","doi":"10.1515/jiip-2021-0038","DOIUrl":"https://doi.org/10.1515/jiip-2021-0038","url":null,"abstract":"Abstract The problem of identification of unknown epidemiological parameters (contagiosity, the initial number of infected individuals, probability of being tested) of an agent-based model of COVID-19 spread in Novosibirsk region is solved and analyzed. The first stage of modeling involves data analysis based on the machine learning approach that allows one to determine correlated datasets of performed PCR tests and number of daily diagnoses and detect some features (seasonality, stationarity, data correlation) to be used for COVID-19 spread modeling. At the second stage, the unknown model parameters that depend on the date of introducing of containment measures are calibrated with the usage of additional measurements such as the number of daily diagnosed and tested people using PCR, their daily mortality rate and other statistical information about the disease. The calibration is based on minimization of the misfit function for daily diagnosed data. The OPTUNA optimization framework with tree-structured Parzen estimator and covariance matrix adaptation evolution strategy is used to minimize the misfit function. Due to ill-posedness of identification problem, the identifiability analysis is carried out to construct the regularization algorithm. At the third stage, the identified parameters of COVID-19 for Novosibirsk region and different scenarios of COVID-19 spread are analyzed in relation to introduced quarantine measures. This kind of modeling can be used to select effective anti-pandemic programs.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"409 - 425"},"PeriodicalIF":1.1,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41749727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces Banach空间中非线性逆问题的一种投影的摄动方法
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-03-31 DOI: 10.1515/jiip-2021-0010
Yuxin Xia, Bo Han, Wei Wang
{"title":"A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces","authors":"Yuxin Xia, Bo Han, Wei Wang","doi":"10.1515/jiip-2021-0010","DOIUrl":"https://doi.org/10.1515/jiip-2021-0010","url":null,"abstract":"Abstract In this paper, we propose and analyze a projected homotopy perturbation method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. To expedite convergence, the approach uses two search directions given by homotopy perturbation iteration, and the new iteration is calculated as the projection of the current iteration onto the intersection of stripes decided by above directions. The method allows to use L 1 {L^{1}} -like penalty terms, which is significant to reconstruct sparsity solutions. Under reasonable conditions, we establish the convergence and regularization properties of the method. Finally, two parameter identification problems are presented to indicate the effectiveness of capturing the property of the sparsity solutions and the acceleration effect of the proposed method.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47583958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Inverse nodal problem for diffusion operator on a star graph with nonhomogeneous edges 非齐次边星图上扩散算子的逆节点问题
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-03-31 DOI: 10.1515/jiip-2022-0094
Sevim Durak
{"title":"Inverse nodal problem for diffusion operator on a star graph with nonhomogeneous edges","authors":"Sevim Durak","doi":"10.1515/jiip-2022-0094","DOIUrl":"https://doi.org/10.1515/jiip-2022-0094","url":null,"abstract":"Abstract In this study, a diffusion operator is investigated on a star graph with nonhomogeneous edges. First, the behaviors of sufficiently large eigenvalues are learned, and then the solution of the inverse problem is given to determine the potential functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and to obtain a constructive solution to the inverse problems of this class.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45125270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Inverse problem for the Atangana–Baleanu fractional differential equation Atangana-Baleanu分数阶微分方程的反问题
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-03-31 DOI: 10.1515/jiip-2022-0025
Santosh Ruhil, Muslim Malik
{"title":"Inverse problem for the Atangana–Baleanu fractional differential equation","authors":"Santosh Ruhil, Muslim Malik","doi":"10.1515/jiip-2022-0025","DOIUrl":"https://doi.org/10.1515/jiip-2022-0025","url":null,"abstract":"Abstract In this manuscript, we examine a fractional inverse problem of order 0 < ρ < 1 {0<rho<1} in a Banach space, including the Atangana–Baleanu fractional derivative in the Caputo sense. We use an overdetermined condition on a mild solution to identify the parameter. The major strategies for determining the outcome are a direct approach using the Volterra integral equation for sufficiently regular data. For less regular data, an optimal control approach uses Euler–Lagrange (EL) equations for the fractional order control problem (FOCP) and a numerical approach for solving FOCP. At last, a numerical example is provided in the support of our results.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42351649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation Kuramoto–Sivashinsky方程中时间依赖源项的识别
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-03-31 DOI: 10.1515/jiip-2022-0030
K. Cao
{"title":"Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation","authors":"K. Cao","doi":"10.1515/jiip-2022-0030","DOIUrl":"https://doi.org/10.1515/jiip-2022-0030","url":null,"abstract":"Abstract The determination of an unknown time-dependent source term is investigated in a Kuramoto–Sivashinsky equation from given additional integral-type measurement. Based on Schauder’s fixed point theorem, the existence and uniqueness of such inverse problem are obtained under certain assumptions on the input data. In order to calculate the unknown source term, a time-discrete system is established, and its solution shall be applied to approximate the unknown quantity. The existence, uniqueness and some estimates to the time-discrete system are derived, and the convergence rates are deduced rigorously for both exact and noisy observation, respectively. Finally, the theoretical convergence rate results are verified, and accurate and stable solutions to the inverse problem are computed numerically by two numerical experiments.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44857733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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