Inverse Problems最新文献_第8页

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application 用过参数化投射梯度下降法估计离网稀疏尖峰：理论与应用

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-14 DOI: 10.1088/1361-6420/ad33e4

Pierre-Jean Bénard, Yann Traonmilin, Jean-François Aujol, Emmanuel Soubies

引用次数: 2

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":null,"pages":null},"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":null,"pages":null},"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

Machine learning for structural design models of continuous beam systems via inﬂuence zones 通过影响区对连续梁系统结构设计模型进行机器学习

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-12 DOI: 10.1088/1361-6420/ad3334

A. Gallet, Andrew Liew, Iman Hajirasouliha, Danny Smyl

{"title":"Machine learning for structural design models of continuous beam systems via inﬂuence zones","authors":"A. Gallet, Andrew Liew, Iman Hajirasouliha, Danny Smyl","doi":"10.1088/1361-6420/ad3334","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3334","url":null,"abstract":"\u0000 This work develops a machine learned structural design model for continuous beam systems from the inverse problem perspective. After demarcating between forward, optimisation and inverse machine learned operators, the investigation proposes a novel methodology based on the recently developed influence zone concept which represents a fundamental shift in approach compared to traditional structural design methods. The aim of this approach is to conceptualise a non-iterative structural design model that predicts cross-section requirements for continuous beam systems of arbitrary system size. After generating a dataset of known solutions, an appropriate neural network architecture is identified, trained, and tested against unseen data. The results show a mean absolute percentage testing error of 1.6% for cross-section property predictions, along with a good ability of the neural network to generalise well to structural systems of variable size. The CBeamXP dataset generated in this work and an associated python-based neural network training script are available at an open-source data repository to allow for the reproducibility of results and to encourage further investigations.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250592","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":null,"pages":null},"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":null,"pages":null},"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

Image analysis and resolution for detection-based synthetic-aperture passive source localization 基于探测的合成孔径被动源定位的图像分析和分辨率

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-07 DOI: 10.1088/1361-6420/ad3165

Margaret Cheney, Louis L. Scharf, Matthew Rhilinger, Cole Moore, Andre Celestin

{"title":"Image analysis and resolution for detection-based synthetic-aperture passive source localization","authors":"Margaret Cheney, Louis L. Scharf, Matthew Rhilinger, Cole Moore, Andre Celestin","doi":"10.1088/1361-6420/ad3165","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3165","url":null,"abstract":"\u0000 This paper follows a detection-theoretic approach for using synthetic- aperture measurements, made at multiple moving passive receivers, in order to form an image showing the locations of stationary sources that are radiating unknown electromagnetic or acoustic waves. The paper starts with a physics- based model for the propagating fields, and, following the general approach of [1, 2], derives a detection statistic that is used for the image formation. This detection statistic is a quadratic function of the data. Each point in the scene is tested as a possible hypothesized location for a source, and the detection statistic is plotted as a function of location. Because this image formation process is nonlinear, the standard linear methods for determining resolution cannot be applied. This paper shows how to analyze the detection image by first writing the noiseless image as a coherent sum of shifted complex ambiguity functions of the source waveform. The paper then develops a technique for calculating image resolution; resolution is found to depend on the sensor-source geometry and also on the properties (bandwidth and temporal duration) of the source waveform. Optimal filtering of the image is given, but a simple example suggests that optimal filtering may have little effect. Analysis is also given for the case in which multiple sources are present.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140259089","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