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Inverse Problems & Imaging最新文献

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Inverse boundary value problems for polyharmonic operators with non-smooth coefficients 非光滑系数多谐算子的反边值问题
Inverse Problems & Imaging Pub Date : 2021-08-26 DOI: 10.3934/ipi.2022006
R. M. Brown, L. Gauthier
{"title":"Inverse boundary value problems for polyharmonic operators with non-smooth coefficients","authors":"R. M. Brown, L. Gauthier","doi":"10.3934/ipi.2022006","DOIUrl":"https://doi.org/10.3934/ipi.2022006","url":null,"abstract":"We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115832047","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: 3
Photoacoustic tomography in attenuating media with partial data 部分数据衰减介质中的光声层析成像
Inverse Problems & Imaging Pub Date : 2021-01-21 DOI: 10.3934/ipi.2022013
Benjamin Palacios
{"title":"Photoacoustic tomography in attenuating media with partial data","authors":"Benjamin Palacios","doi":"10.3934/ipi.2022013","DOIUrl":"https://doi.org/10.3934/ipi.2022013","url":null,"abstract":"The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and some advances have been made on the topic. In particular, stability inequalities have been proposed for the inverse problem of initial source recovery with partial observations under the assumption of unique determination of the initial pressure. The main goal of this work is to fill this gap, this is, we prove the uniqueness property for the inverse problem and establish the associated stability estimates as well. The problem of reconstructing the initial condition of acoustic waves in the complete-data setting is revisited and a new Neumann series reconstruction formula is obtained for the case of partial observations in a semi-bounded geometry. A numerical simulation is also included to test the method.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124616100","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: 1
An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method 热成像中三维热方程的反问题及封闭法
Inverse Problems & Imaging Pub Date : 2014-11-01 DOI: 10.3934/ipi.2014.8.1073
Masaru Ikehata, M. Kawashita
{"title":"An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method","authors":"Masaru Ikehata, M. Kawashita","doi":"10.3934/ipi.2014.8.1073","DOIUrl":"https://doi.org/10.3934/ipi.2014.8.1073","url":null,"abstract":"This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {it single} set of the temperature and heat flux on the lateral boundary for a fixed observation time is given as an observation datum. It is shown that this datum yields the minimum length of broken paths that start at a given point outside the body, go to a point on the boundary of the unknown discontinuity and return to a point on the boundary of the body under some conditions on the input heat flux, the unknown discontinuity and the body. This is new information obtained by using enclosure method.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130235256","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: 13
A fast modified Newton's method for curvature based denoising of 1D signals 基于曲率的一维信号去噪的快速改进牛顿方法
Inverse Problems & Imaging Pub Date : 2013-09-01 DOI: 10.3934/IPI.2013.7.1075
A. Yip, Wei Zhu
{"title":"A fast modified Newton's method for curvature based denoising of 1D signals","authors":"A. Yip, Wei Zhu","doi":"10.3934/IPI.2013.7.1075","DOIUrl":"https://doi.org/10.3934/IPI.2013.7.1075","url":null,"abstract":"We propose a novel fast numerical method for denoising of 1D signals \u0000based on curvature minimization. Motivated by the \u0000primal-dual formulation for total variation minimization \u0000introduced by Chan, Golub, and Mulet, the proposed method makes \u0000use of some auxiliary variables to reformulate the stiff terms presented \u0000in the Euler-Lagrange equation which is a fourth-order \u0000differential equation. A direct application of Newton's method \u0000to the resulting system of equations often fails to converge. \u0000We propose a modified Newton's iteration which \u0000exhibits local superlinear convergence and global convergence in practical settings. \u0000The method is much faster than other existing methods for the model. \u0000Unlike all other existing methods, it also does not require tuning any additional \u0000parameter besides the model parameter. \u0000Numerical experiments are presented to demonstrate the \u0000effectiveness of the proposed method.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125219987","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: 3
A uniqueness theorem for inverse problems in quasilinear anisotropic media 拟线性各向异性介质反问题的唯一性定理
Inverse Problems & Imaging Pub Date : 1900-01-01 DOI: 10.3934/ipi.2022008
Md. Ibrahim Kholil, Ziqi Sun
{"title":"A uniqueness theorem for inverse problems in quasilinear anisotropic media","authors":"Md. Ibrahim Kholil, Ziqi Sun","doi":"10.3934/ipi.2022008","DOIUrl":"https://doi.org/10.3934/ipi.2022008","url":null,"abstract":"We study the question of whether one can uniquely determine a scalar quasilinear conductivity in an anisotropic medium by making voltage and current measurements at the boundary. This paper is dedicated to the memory of Professor Victor Isakov, who has made enormous contribution to the theory of inverse problem.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122183854","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
Recovering a bounded elastic body by electromagnetic far-field measurements 用电磁远场测量恢复有界弹性体
Inverse Problems & Imaging Pub Date : 1900-01-01 DOI: 10.3934/ipi.2022012
Tielei Zhu, Jiaqing Yang, Bo Zhang
{"title":"Recovering a bounded elastic body by electromagnetic far-field measurements","authors":"Tielei Zhu, Jiaqing Yang, Bo Zhang","doi":"10.3934/ipi.2022012","DOIUrl":"https://doi.org/10.3934/ipi.2022012","url":null,"abstract":"This paper is concerned with the scattering of a time-harmonic electromagnetic wave by a three-dimensional elastic body. The general transmission conditions are considered to model the interaction between the electromagnetic field and the elastic body on the interface by Voigt's model. The existence of a unique solution is first proved in an appropriate Sobolev space by employing the variational method with the classical Fredholm alternative. The inverse problem is then investigated to recover the elastic body by the scattered wave-field data. It is shown that the shape and location of the body is uniquely determined by the fixed energy magnetic (or electric) far-field measurements corresponding to incident plane waves with all polarizations.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123730273","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: 2
A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise 含泊松-拉普拉斯-高斯混合噪声的阿贝尔反演层析成像变分方法
Inverse Problems & Imaging Pub Date : 1900-01-01 DOI: 10.3934/ipi.2022007
Linghai Kong, Suhua Wei
{"title":"A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise","authors":"Linghai Kong, Suhua Wei","doi":"10.3934/ipi.2022007","DOIUrl":"https://doi.org/10.3934/ipi.2022007","url":null,"abstract":"Abel inversion tomography plays an important role in dynamic experiments, while most known studies are started with a single Gaussian assumption. This paper proposes a mixed Poisson-Laplace-Gaussian distribution to characterize the noise in charge-coupled-device (CCD) sensed radiographic data, and develops a multi-convex optimization model to address the reconstruction problem. The proposed model is derived by incorporating varying amplitude Gaussian approximation and expectation maximization algorithm into an infimal convolution process. To solve it numerically, variable splitting and augmented Lagrangian method are integrated into a block coordinate descent framework, in which anisotropic diffusion and additive operator splitting are employed to gain edge preserving and computation efficiency. Supplementarily, a space of functions of adaptive bounded Hessian is introduced to prove the existence and uniqueness of solution to a higher-order regularized, quadratic subproblem. Moreover, a simplified algorithm with higher order regularizer is derived for Poisson noise removal. To illustrate the performance of the proposed algorithms, numerical tests on synthesized and real digital data are performed.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129528206","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: 2
An iterative scheme for imaging acoustic obstacle from phaseless total-field data 无相全场数据成像声障碍物的迭代方法
Inverse Problems & Imaging Pub Date : 1900-01-01 DOI: 10.3934/ipi.2022005
Heping Dong, Deyue Zhang, Yingwei Chi
{"title":"An iterative scheme for imaging acoustic obstacle from phaseless total-field data","authors":"Heping Dong, Deyue Zhang, Yingwei Chi","doi":"10.3934/ipi.2022005","DOIUrl":"https://doi.org/10.3934/ipi.2022005","url":null,"abstract":"In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft or sound-hard obstacle from the modulus of the total-field collected on a measured curve for an incident point source. We propose a system of nonlinear integral equations based iterative scheme to reconstruct both the location and the shape of the obstacle. Several validating numerical examples are provided to illustrate the effectiveness and robustness of the proposed inversion algorithm.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114523923","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
A new anisotropic fourth-order diffusion equation model based on image features for image denoising 一种新的基于图像特征的各向异性四阶扩散方程模型
Inverse Problems & Imaging Pub Date : 1900-01-01 DOI: 10.3934/ipi.2022004
Ying Wen, Jiebao Sun, Zhichang Guo
{"title":"A new anisotropic fourth-order diffusion equation model based on image features for image denoising","authors":"Ying Wen, Jiebao Sun, Zhichang Guo","doi":"10.3934/ipi.2022004","DOIUrl":"https://doi.org/10.3934/ipi.2022004","url":null,"abstract":"Image denoising has always been a challenging task. For performing this task, one of the most effective methods is based on variational PDE. Inspired by the LLT model, we first propose a new adaptive LLT model by adding a weighted function, and then we propose a class of fourth-order diffusion equations based on the new functional. Owing to the adaptive function, the new functional is better than the LLT model and other fourth-order models in terms of edge preservation. While generalizing the Euler-Lagrange equation of the new functional, we discuss a new fourth-order diffusion framework for image denoising. Different from those of other fourth-order diffusion models, the new diffusion coefficients depend on the first-order and second-order derivatives, which can preserve edges and smooth images, respectively. Regarding numerical implementations, we first design an explicit scheme for the proposed model. However, fourth-order diffusion equations require strict stability conditions, and the number of iterations needed is considerable. Consequently, we apply the fast explicit diffusion algorithm (FED) to the explicit scheme to reduce the time consumption of the proposed approach. Furthermore, the additive operator splitting (AOS) scheme is applied for the numerical implementation, and it is the most efficient among all of our algorithms. Finally, compared with other models, the new model exhibits superior effectiveness and efficiency.","PeriodicalId":435862,"journal":{"name":"Inverse Problems & Imaging","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121111765","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: 7
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