Inverse Problems最新文献_第7页

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

Bayesian view on the training of invertible residual networks for solving linear inverse problems * 贝叶斯视角下用于解决线性逆问题的可逆残差网络的训练 *

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-06 DOI: 10.1088/1361-6420/ad2aaa

Clemens Arndt, Sören Dittmer, Nick Heilenkötter, Meira Iske, Tobias Kluth, Judith Nickel

{"title":"Bayesian view on the training of invertible residual networks for solving linear inverse problems *","authors":"Clemens Arndt, Sören Dittmer, Nick Heilenkötter, Meira Iske, Tobias Kluth, Judith Nickel","doi":"10.1088/1361-6420/ad2aaa","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2aaa","url":null,"abstract":"Learning-based methods for inverse problems, adapting to the data’s inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works address the issue of theoretical guarantees. Recently, Arndt <italic toggle=\"yes\">et al</italic> (2023 <italic toggle=\"yes\">Inverse Problems</italic>\u0000<bold>39</bold> 125018) exploited invertible residual networks (iResNets) to learn provably convergent regularizations given reasonable assumptions. They enforced these guarantees by approximating the linear forward operator with an iResNet. Supervised training on relevant samples introduces data dependency into the approach. An open question in this context is to which extent the data’s inherent structure influences the training outcome, i.e. the learned reconstruction scheme. Here, we address this delicate interplay of training design and data dependency from a Bayesian perspective and shed light on opportunities and limitations. We resolve these limitations by analyzing reconstruction-based training of the inverses of iResNets, where we show that this optimization strategy introduces a level of data-dependency that cannot be achieved by approximation training. We further provide and discuss a series of numerical experiments underpinning and extending the theoretical findings.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"107 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315293","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

Inverse problem for Love waves in a layered, elastic half-space 层状弹性半空间中爱波的逆问题

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-05 DOI: 10.1088/1361-6420/ad2781

Maarten V de Hoop, Josselin Garnier, Alexei Iantchenko, Julien Ricaud

引用次数: 0

Generalized variational framework with minimax optimization for parametric blind deconvolution 参数盲解卷的最小优化广义变分框架

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-05 DOI: 10.1088/1361-6420/ad2c30

Qichao Cao, Deren Han, Xiangfeng Wang, Wenxing Zhang

引用次数: 0

The monotonicity method for inclusion detection and the time harmonic elastic wave equation 包含检测的单调性方法和时谐弹性波方程