Inverse Problems最新文献_第7页

Local data inverse problem for the polyharmonic operator with anisotropic perturbations 具有各向异性扰动的多谐算子的局部数据逆问题

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-19 DOI: 10.1088/1361-6420/ad3164

Sombuddha Bhattacharyya, Pranav Kumar

引用次数: 0

Reconstruction of degenerate conductivity region for parabolic equations 抛物方程退化传导区域的重构

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-15 DOI: 10.1088/1361-6420/ad308a

Piermarco Cannarsa, Anna Doubova, Masahiro Yamamoto

引用次数: 0

Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary * 确定未知时变边界的反随机抛物线问题的稳定性估计 *

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-15 DOI: 10.1088/1361-6420/ad2d72

Zhonghua Liao, Qi Lü

引用次数: 0

Shape and orientation classification of objects based on their electromagnetic signatures using convolutional neural networks 利用卷积神经网络根据电磁特征对物体进行形状和方向分类

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-13 DOI: 10.1088/1361-6420/ad2ec9

Yasmina Zaky, Nicolas Fortino, Benoit Miramond, Jean-Yves Dauvignac

引用次数: 0

Inversion of a restricted transverse ray transform with sources on a curve 曲线上有源的受限横向射线变换的反演

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-12 DOI: 10.1088/1361-6420/ad2ecb

Rohit Kumar Mishra, Chandni Thakkar

{"title":"Inversion of a restricted transverse ray transform with sources on a curve","authors":"Rohit Kumar Mishra, Chandni Thakkar","doi":"10.1088/1361-6420/ad2ecb","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2ecb","url":null,"abstract":"In this paper, a restricted transverse ray transform acting on vector and symmetric <italic toggle=\"yes\">m</italic>-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric <italic toggle=\"yes\">m</italic>-tensor fields in <inline-formula>\u0000<tex-math><?CDATA $mathbb{R}^3$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ipad2ecbieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and vector fields in <inline-formula>\u0000<tex-math><?CDATA $mathbb{R}^n$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ipad2ecbieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. We restrict the transverse ray transform to all lines going through a fixed curve <italic toggle=\"yes\">γ</italic> that satisfies the Kirillov–Tuy condition. We show that the known restricted data can be used to reconstruct a specific weighted Radon transform of the unknown vector/tensor field’s components, which we then use to explicitly recover the unknown field.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"33 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315577","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

On mathematical problems of two-coefficient inverse problems of ultrasonic tomography 论超声波断层扫描双系数逆问题的数学问题

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-12 DOI: 10.1088/1361-6420/ad2aa9

Alexander V Goncharsky, Sergey Y Romanov, Sergey Y Seryozhnikov

{"title":"On mathematical problems of two-coefficient inverse problems of ultrasonic tomography","authors":"Alexander V Goncharsky, Sergey Y Romanov, Sergey Y Seryozhnikov","doi":"10.1088/1361-6420/ad2aa9","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2aa9","url":null,"abstract":"This paper proves the theorem of uniqueness for the solution of a coefficient inverse problem for the wave equation in (with two unknown coefficients: speed of sound and absorption. The original nonlinear coefficient inverse problem is reduced to an equivalent system of two uniquely solvable linear integral equations of the first kind with respect to the sound speed and absorption coefficients. Estimates are made, substantiating the multistage method for two unknown coefficients. These estimates show that given sufficiently low frequencies and small inhomogeneities, the residual functional for the nonlinear inverse problem approaches a convex one. This solution method for nonlinear coefficient inverse problems is not linked to the limit approach as frequency tends to zero, but assumes solving the inverse problem using sufficiently low, but not zero, frequencies at the first stage. For small inhomogeneities that are typical, for instance, for medical tasks, carrying out real experiments at such frequencies does not present major difficulties. The capabilities of the method are demonstrated on a model inverse problem with unknown sound speed and absorption coefficients. The method effectively solves the nonlinear problem with parameter values typical for tomographic diagnostics of soft tissues in medicine. A resolution of approximately 2 mm was achieved using an average sounding pulse wavelength of 5 mm.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"63 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315428","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

Adaptive tempered reversible jump algorithm for Bayesian curve fitting 贝叶斯曲线拟合的自适应调节可逆跳变算法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-11 DOI: 10.1088/1361-6420/ad2cf7

Zhiyao Tian, Anthony Lee, Shunhua Zhou

{"title":"Adaptive tempered reversible jump algorithm for Bayesian curve fitting","authors":"Zhiyao Tian, Anthony Lee, Shunhua Zhou","doi":"10.1088/1361-6420/ad2cf7","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2cf7","url":null,"abstract":"Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without appropriately tuned proposals. As a remedy, we present an adaptive RJMCMC algorithm for the curve fitting problems by extending the adaptive Metropolis sampler from a fixed-dimensional to a trans-dimensional case. In this presented algorithm, both the size and orientation of the proposal function can be automatically adjusted in the sampling process. Specifically, the curve fitting setting allows for the approximation of the posterior covariance of the <italic toggle=\"yes\">a priori</italic> unknown function on a representative grid of points. This approximation facilitates the definition of efficient proposals. In addition, we introduce an auxiliary-tempered version of this algorithm via non-reversible parallel tempering. To evaluate the algorithms, we conduct numerical tests involving a series of controlled experiments. The results demonstrate that the adaptive algorithms exhibit significantly higher efficiency compared to the conventional ones. Even in cases where the posterior distribution is highly complex, leading to ineffective convergence in the auxiliary-tempered conventional RJMCMC, the proposed auxiliary-tempered adaptive RJMCMC performs satisfactorily. Furthermore, we present a realistic inverse example to test the algorithms. The successful application of the adaptive algorithm distinguishes it again from the conventional one that fails to converge effectively even after millions of iterations.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315617","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

Recovering coefficients in a system of semilinear Helmholtz equations from internal data 从内部数据中恢复半线性亥姆霍兹方程组的系数

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-08 DOI: 10.1088/1361-6420/ad2cf9

Kui Ren, Nathan Soedjak

引用次数: 0

A structured L-BFGS method and its application to inverse problems 结构化 L-BFGS 方法及其在逆问题中的应用

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-07 DOI: 10.1088/1361-6420/ad2c31

Florian Mannel, Hari Om Aggrawal, Jan Modersitzki

{"title":"A structured L-BFGS method and its application to inverse problems","authors":"Florian Mannel, Hari Om Aggrawal, Jan Modersitzki","doi":"10.1088/1361-6420/ad2c31","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2c31","url":null,"abstract":"Many inverse problems are phrased as optimization problems in which the objective function is the sum of a data-fidelity term and a regularization. Often, the Hessian of the fidelity term is computationally unavailable while the Hessian of the regularizer allows for cheap matrix-vector products. In this paper, we study an L-BFGS method that takes advantage of this structure. We show that the method converges globally without convexity assumptions and that the convergence is linear under a Kurdyka–Łojasiewicz-type inequality. In addition, we prove linear convergence to cluster points near which the objective function is strongly convex. To the best of our knowledge, this is the first time that linear convergence of an L-BFGS method is established in a non-convex setting. The convergence analysis is carried out in infinite dimensional Hilbert space, which is appropriate for inverse problems but has not been done before. Numerical results show that the new method outperforms other structured L-BFGS methods and classical L-BFGS on non-convex real-life problems from medical image registration. It also compares favorably with classical L-BFGS on ill-conditioned quadratic model problems. An implementation of the method is freely available.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"19 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315621","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

Bi-level iterative regularization for inverse problems in nonlinear PDEs 非线性 PDE 逆问题的双级迭代正则化

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-06 DOI: 10.1088/1361-6420/ad2905

Tram Thi Ngoc Nguyen

引用次数: 0