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Journal of Inverse and Ill-Posed Problems最新文献

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The problem of determining multiple coefficients in an ultrahyperbolic equation 超双曲方程中多个系数的确定问题
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-27 DOI: 10.1515/jiip-2022-0091
Fikret Gölgeleyen
{"title":"The problem of determining multiple coefficients in an ultrahyperbolic equation","authors":"Fikret Gölgeleyen","doi":"10.1515/jiip-2022-0091","DOIUrl":"https://doi.org/10.1515/jiip-2022-0091","url":null,"abstract":"Abstract In this article, we discuss an inverse problem of determining unknown coefficients of the first-order derivatives in an ultrahyperbolic equation. By a finite set of measurements, we prove the uniqueness of solution of the problem in semi-geodesic coordinates under some conditions on the principal coefficients of the equation. Our main tool is a Carleman estimate.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49094549","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
Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces Banach空间中具有冻结导数的非精确Newton-Landweber迭代的收敛性分析
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-27 DOI: 10.1515/jiip-2023-0002
Gaurav Mittal, Ankik Kumar Giri
{"title":"Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces","authors":"Gaurav Mittal, Ankik Kumar Giri","doi":"10.1515/jiip-2023-0002","DOIUrl":"https://doi.org/10.1515/jiip-2023-0002","url":null,"abstract":"Abstract In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well as Banach spaces without using any extra smoothness condition. Finally, we compare our convergence rates results with that of several other frozen methods proposed in the literature to solve inverse problems.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43993780","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
Stability properties for a class of inverse problems 一类反问题的稳定性
4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-14 DOI: 10.1515/jiip-2022-0015
Darko Volkov
{"title":"Stability properties for a class of inverse problems","authors":"Darko Volkov","doi":"10.1515/jiip-2022-0015","DOIUrl":"https://doi.org/10.1515/jiip-2022-0015","url":null,"abstract":"Abstract We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">A</m:mi> <m:mi>m</m:mi> </m:msub> </m:math> mathcal{A}_{m} depending nonlinearly on a parameter 𝑚 and operating on a function 𝑢. In the inversion step, both 𝑢 and 𝑚 are unknown, but we are only interested in recovering 𝑚. We discuss examples of such inverse problems for the elasticity equation with applications to seismology and for the inverse scattering problem in electromagnetic theory. Assuming a few injectivity and regularity properties for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">A</m:mi> <m:mi>m</m:mi> </m:msub> </m:math> mathcal{A}_{m} , we prove that the inverse problem with a finite number of data points is solvable and that the solution is Lipschitz stable in the data. We show a reconstruction example illustrating the use of neural networks.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860435","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
Regularization operators versus regularization strategies 正则化操作符与正则化策略
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI: 10.1515/jiip-2022-0073
Thi-An Nguyen, C. Law
{"title":"Regularization operators versus regularization strategies","authors":"Thi-An Nguyen, C. Law","doi":"10.1515/jiip-2022-0073","DOIUrl":"https://doi.org/10.1515/jiip-2022-0073","url":null,"abstract":"Abstract In this note, we shall compare two important concepts of “regularization operators” and “regularization strategies” that appear in different classical monographs. The definition of a regularization operator is related to the Moore–Penrose inverse of the operator. In general, a regularization operator is a regularization strategy. We shall show that the converse is also true under some conditions. It is interesting to note that these two systems share analogous properties.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"625 - 629"},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47438635","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
On the recovery of internal source for an elliptic system by neural network approximation 用神经网络近似恢复椭圆系统的内源
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI: 10.1515/jiip-2022-0005
Hui Zhang, Jijun Liu
{"title":"On the recovery of internal source for an elliptic system by neural network approximation","authors":"Hui Zhang, Jijun Liu","doi":"10.1515/jiip-2022-0005","DOIUrl":"https://doi.org/10.1515/jiip-2022-0005","url":null,"abstract":"Abstract Consider a source detection problem for a diffusion system at its stationary status, which is stated as the inverse source problem for an elliptic equation from the measurement of the solution specified only in part of the domain. For this linear ill-posed problem, we propose to reconstruct the interior source applying neural network algorithm, which projects the problem into a finite-dimensional space by approximating both the unknown source and the corresponding solution in terms of two neural networks. By minimizing a novel loss function consisting of PDE-fit and data-fit terms but without the boundary condition fit, the modified deep Galerkin method (MDGM) is applied to solve this problem numerically. Based on the stability result for the analytic extension of the solution, we strictly estimate the generalization error caused by the MDGM algorithm employing the property of conditional stability and the regularity of the solution. Numerical experiments show that we can obtain satisfactory reconstructions even in higher-dimensional cases, and validate the effectiveness of the proposed algorithm for different model configurations. Moreover, our algorithm is stable with respect to noisy inversion input data for the noise in various structures.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49415441","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: 1
The game model with multi-task for image denoising and edge extraction 多任务博弈模型用于图像去噪和边缘提取
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI: 10.1515/jiip-2022-0051
Wenyan Wei, Xiangchu Feng, Bingzhe Wei
{"title":"The game model with multi-task for image denoising and edge extraction","authors":"Wenyan Wei, Xiangchu Feng, Bingzhe Wei","doi":"10.1515/jiip-2022-0051","DOIUrl":"https://doi.org/10.1515/jiip-2022-0051","url":null,"abstract":"Abstract Image denoising and edge extraction are two main tasks in image processing. In this paper, a game model is proposed to solve the image denoising and edge extraction, which combines an adaptive improved total variation (AdITV) model for image denoising and a global sparse gradient (GSG) model for edge extraction. The AdITV model is a forward-and-backward diffusion model. In fact, forward diffusion is applied to the homogeneous region to denoise, and backward diffusion is applied to the edge region to enhance the edge. A unified explicit discrete scheme is established in this paper to solve the AdITV model, which is compatible to forward diffusion and backward diffusion. The stability of the scheme is proved. On the other hand, GSG is a functional model based on sparse representation, which is robust to extract edges under the influence of noise. AdITV and GSG are chosen as two components of the game model. The alternate iteration method is used to solve the game problem. The convergence of the algorithm is proved and numerical experiments show the effectiveness of the model.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41733770","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
On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition 具有终超定条件的线性化Navier-Stokes方程组的反问题
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI: 10.1515/jiip-2022-0065
M. Jenaliyev, M. Bektemesov, M. Yergaliyev
{"title":"On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition","authors":"M. Jenaliyev, M. Bektemesov, M. Yergaliyev","doi":"10.1515/jiip-2022-0065","DOIUrl":"https://doi.org/10.1515/jiip-2022-0065","url":null,"abstract":"Abstract The theory of inverse problems is an actively studied area of modern differential equation theory. This paper studies the solvability of the inverse problem for a linearized system of Navier–Stokes equations in a cylindrical domain with a final overdetermination condition. Our approach is to reduce the inverse problem to a direct problem for a loaded equation. In contrast to the well-known works in this field, our approach is to find an equation for a loaded term whose solvability condition provides the solvability of the original inverse problem. At the same time, the classical theory of spectral decomposition of unbounded self-adjoint operators is actively used. Concrete examples demonstrate that the assertions of our theorems naturally develop and complement the known results on inverse problems. Various cases are considered when the known coefficient on the right-hand side of the equation depends only on time or both on time and a spatial variable. Theorems establishing new sufficient conditions for the unique solvability of the inverse problem under consideration are proved.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"611 - 624"},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43362515","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
On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method 基于加权自导向tv正则化方法的线性各向同性弹性结构lam<s:1>参数辨识
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI: 10.1515/jiip-2021-0050
V. Markaki, D. Kourounis, A. Charalambopoulos
{"title":"On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method","authors":"V. Markaki, D. Kourounis, A. Charalambopoulos","doi":"10.1515/jiip-2021-0050","DOIUrl":"https://doi.org/10.1515/jiip-2021-0050","url":null,"abstract":"Abstract Recently in [V. Markaki, D. Kourounis and A. Charalambopoulos, A dual self-monitored reconstruction scheme on the TV mathrm{TV} -regularized inverse conductivity problem, IMA J. Appl. Math. 86 2021, 3, 604–630], a novel reconstruction scheme has been developed for the solution of the inclusion problem in the inverse conductivity problem on the basis of a weighted self-guided regularization process generalizing the total variation approach. The present work extends this concept by implementing and investigating its applicability in the two-dimensional elasticity setting. To this end, we employ the framework of the reconstruction of linear and isotropic elastic structures described by their Lamé parameters. Numerical examples of increasingly challenging geometric complexities illustrate the enhanced accuracy and efficiency of the method.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44699685","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
A dynamical method for optimal control of the obstacle problem 障碍物问题最优控制的一种动力学方法
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-31 DOI: 10.1515/jiip-2020-0135
Qinghua Ran, Xiaoliang Cheng, R. Gong, Ye Zhang
{"title":"A dynamical method for optimal control of the obstacle problem","authors":"Qinghua Ran, Xiaoliang Cheng, R. Gong, Ye Zhang","doi":"10.1515/jiip-2020-0135","DOIUrl":"https://doi.org/10.1515/jiip-2020-0135","url":null,"abstract":"Abstract In this paper, we consider the numerical method for an optimal control problem governed by an obstacle problem. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem with a simple method. The connection between the two formulations is established through some convergence results. A sufficient condition is derived to decide whether a solution of the first-order optimality system is a global minimum. The method with a second-order in time dissipative system is developed to solve the optimality system numerically. Several numerical examples are reported to show the effectiveness of the proposed method.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"577 - 594"},"PeriodicalIF":1.1,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48984158","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
On recovery of an unbounded bi-periodic interface for the inverse fluid-solid interaction scattering problem 反流固相互作用散射问题的无界双周期界面的恢复
IF 1.1 4区 数学
Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-03 DOI: 10.1515/jiip-2021-0070
Yan-li Cui, F. Qu, C. Wei
{"title":"On recovery of an unbounded bi-periodic interface for the inverse fluid-solid interaction scattering problem","authors":"Yan-li Cui, F. Qu, C. Wei","doi":"10.1515/jiip-2021-0070","DOIUrl":"https://doi.org/10.1515/jiip-2021-0070","url":null,"abstract":"Abstract This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"431 - 440"},"PeriodicalIF":1.1,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41799710","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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