Inverse Problems最新文献

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Fourier method for inverse source problem using correlation of passive measurements* 利用被动测量相关性解决逆源问题的傅立叶方法*
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-04 DOI: 10.1088/1361-6420/ad6fc7
Faouzi Triki, Kristoffer Linder-Steinlein, Mirza Karamehmedović
{"title":"Fourier method for inverse source problem using correlation of passive measurements*","authors":"Faouzi Triki, Kristoffer Linder-Steinlein, Mirza Karamehmedović","doi":"10.1088/1361-6420/ad6fc7","DOIUrl":"https://doi.org/10.1088/1361-6420/ad6fc7","url":null,"abstract":"We consider the inverse source problem for the time-dependent, constant-coefficient wave equation with Cauchy data and passive cross-correlation data.We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we show that the cross-correlation solves a wave equation, and we reconstruct the cross-correlation from boundary data to recover the source in the original Cauchy wave equation. In addition, we show the inverse source problem is ill-posed and suffers from non-uniqueness when the mean of the source is zero and provide a uniqueness result and stability estimate in case of non-zero mean sources.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"21 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226717","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
Enhanced microscale hydrodynamic near-cloaking using electro-osmosis 利用电渗技术增强微尺度流体力学近包裹性
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-02 DOI: 10.1088/1361-6420/ad7283
Hongyu Liu, Zhi-Qiang Miao, Guang-Hui Zheng
{"title":"Enhanced microscale hydrodynamic near-cloaking using electro-osmosis","authors":"Hongyu Liu, Zhi-Qiang Miao, Guang-Hui Zheng","doi":"10.1088/1361-6420/ad7283","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7283","url":null,"abstract":"In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the relationship of shapes is quantified more accurately by recursive formulas. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking. Additionally, the concept of cloaking has efficient applications in the field of microfluidics, including drag reduction, microfluidic manipulation, and biological tissue coculture.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"22 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210290","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
Phase retrieval and phaseless inverse scattering with background information 带背景信息的相位检索和无相位反向散射
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-30 DOI: 10.1088/1361-6420/ad6fc6
Thorsten Hohage, Roman G Novikov, Vladimir N Sivkin
{"title":"Phase retrieval and phaseless inverse scattering with background information","authors":"Thorsten Hohage, Roman G Novikov, Vladimir N Sivkin","doi":"10.1088/1361-6420/ad6fc6","DOIUrl":"https://doi.org/10.1088/1361-6420/ad6fc6","url":null,"abstract":"We consider the problem of finding a compactly supported potential in the multidimensional Schrödinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier transform on a ball. To compensate for the missing phase information we use the method of <italic toggle=\"yes\">a priori</italic> known background scatterers. In particular, we propose an iterative scheme for finding the potential from measurements of a single differential scattering cross section corresponding to the sum of the unknown potential and a known background potential, which is sufficiently disjoint. If this condition is relaxed, then we give similar results for finding the potential from additional monochromatic measurements of the differential scattering cross section of the unknown potential without the background potential. The performance of the proposed algorithms is demonstrated in numerical examples. In the present work we significantly advance theoretically and numerically studies of Agaltsov <italic toggle=\"yes\">et al</italic> (2019 <italic toggle=\"yes\">Inverse Problems</italic> <bold>35</bold> 24001) and Novikov and Sivkin (2021 <italic toggle=\"yes\">Inverse Problems</italic> <bold>37</bold> 055011).","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210298","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
A Kirchhoff Migration scheme for elastic obstacle identification 用于弹性障碍物识别的基尔霍夫迁移方案
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-29 DOI: 10.1088/1361-6420/ad6fc8
Daniel Rabinovich, Dan Givoli
{"title":"A Kirchhoff Migration scheme for elastic obstacle identification","authors":"Daniel Rabinovich, Dan Givoli","doi":"10.1088/1361-6420/ad6fc8","DOIUrl":"https://doi.org/10.1088/1361-6420/ad6fc8","url":null,"abstract":"Kirchhoff Migration (KM), sometimes called Arrival (or Travel) Time Imaging, is a basic and popular imaging technique based on the arrival time of waves from given sources to given sensors. It is commonly used in the fields of underwater acoustics and solid earth geophysics, for both subsurface structure analysis and for identifying unknown local obstacles (scatterers) in the medium. The present paper concentrates on the latter application. For acoustics, the KM algorithm is extremely simple and efficient, although it usually produces a rather crude image, which is the reason for its use as the method of choice when high resolution is not needed, or as a fast technique to produce an initial guess for a more sophisticated imaging method. For elasticity, KM is much more involved, as the arrival-time algorithm is not obvious, mainly since there is more than one wave speed at each spatial point. In this paper, a new KM scheme is proposed for obstacle identification in an isotropic piecewise-homogeneous elastic medium. The scheme is based on measuring two quantities that are second-order operators of the displacement field, which are related to P and S waves, and applying the acoustic KM algorithm to each of them, with the appropriate wave speed. It is demonstrated numerically that the operator related to S waves results in very good identification in many cases. The fact that measurements based on the S-related operator are preferred over those based on the P-related operator is an empirical observation, and awaits full analysis, although a partial explanation is given here.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226718","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 source problem for discrete Helmholtz equation 离散赫尔姆霍兹方程的反源问题
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-28 DOI: 10.1088/1361-6420/ad7054
Roman Novikov, Basant Lal Sharma
{"title":"Inverse source problem for discrete Helmholtz equation","authors":"Roman Novikov, Basant Lal Sharma","doi":"10.1088/1361-6420/ad7054","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7054","url":null,"abstract":"We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice <inline-formula>\u0000<tex-math><?CDATA $mathbb{Z}^d$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"ipad7054ieqn1.gif\"></inline-graphic></inline-formula>, <inline-formula>\u0000<tex-math><?CDATA $d unicode{x2A7E} 1$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>d</mml:mi><mml:mtext>⩾</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"ipad7054ieqn2.gif\"></inline-graphic></inline-formula>. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"61 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210299","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
Pseudo-differential integral autoencoder network for inverse PDE operators 用于逆 PDE 算子的伪微分积分自动编码器网络
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-28 DOI: 10.1088/1361-6420/ad7056
Ke Chen, Jasen Lai, Chunmei Wang
{"title":"Pseudo-differential integral autoencoder network for inverse PDE operators","authors":"Ke Chen, Jasen Lai, Chunmei Wang","doi":"10.1088/1361-6420/ad7056","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7056","url":null,"abstract":"Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural network, ‘pseudo-differential IAEnet’ (pd-IAEnet), which draws inspiration from pseudo-differential operators. pd-IAEnet achieves significantly enhanced computational speed and accuracy with fewer parameters compared to conventional models. Extensive benchmark evaluations are conducted across a range of inverse problems, including electrical impedance tomography, optical tomography, and seismic imaging, consistently demonstrating pd-IAEnet’s superior accuracy. Notably, pd-IAEnet exhibits robustness in the presence of measurement noise, a critical characteristic for real-world applications. An exceptional feature is its discretization invariance, enabling effective training on data from diverse discretization schemes while maintaining accuracy on different meshes. In summary, pd-IAEnet offers a potent and efficient solution for addressing inverse PDE problems, contributing to improved computational efficiency, robustness, and adaptability to a wide array of data sources.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"61 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210310","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
An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth 在没有地面实况的情况下比较维纳-亨特解卷积模型的最佳贝叶斯策略
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-27 DOI: 10.1088/1361-6420/ad6a35
B Harroué, J-F Giovannelli, M Pereyra
{"title":"An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth","authors":"B Harroué, J-F Giovannelli, M Pereyra","doi":"10.1088/1361-6420/ad6a35","DOIUrl":"https://doi.org/10.1088/1361-6420/ad6a35","url":null,"abstract":"This paper considers the quantitative comparison of several alternative models to perform deconvolution in situations where there is no ground truth data available. With applications to very large data sets in mind, we focus on linear deconvolution models based on a Wiener filter. Although comparatively simple, such models are widely prevalent in large scale setting such as high-resolution image restoration because they provide an excellent trade-off between accuracy and computational effort. However, in order to deliver accurate solutions, the models need to be properly calibrated in order to capture the covariance structure of the unknown quantity of interest and of the measurement error. This calibration often requires onerous controlled experiments and extensive expert supervision, as well as regular recalibration procedures. This paper adopts an unsupervised Bayesian statistical approach to model assessment that allows comparing alternative models by using only the observed data, without the need for ground truth data or controlled experiments. Accordingly, the models are quantitatively compared based on their posterior probabilities given the data, which are derived from the marginal likelihoods or <italic toggle=\"yes\">evidences</italic> of the models. The computation of these evidences is highly non-trivial and this paper consider three different strategies to address this difficulty—a Chib approach, Laplace approximations, and a truncated harmonic expectation—all of which efficiently implemented by using a Gibbs sampling algorithm specialised for this class of models. In addition to enabling unsupervised model selection, the output of the Gibbs sampler can also be used to automatically estimate unknown model parameters such as the variance of the measurement error and the power of the unknown quantity of interest. The proposed strategies are demonstrated on a range of image deconvolution problems, where they are used to compare different modelling choices for the instrument’s point spread function and covariance matrices for the unknown image and for the measurement error.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"36 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226719","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
Increasing stability of the acoustic and elastic inverse source problems in multi-layered media 提高多层介质中声学和弹性反源问题的稳定性
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-27 DOI: 10.1088/1361-6420/ad7055
Tianjiao Wang, Xiang Xu, Yue Zhao
{"title":"Increasing stability of the acoustic and elastic inverse source problems in multi-layered media","authors":"Tianjiao Wang, Xiang Xu, Yue Zhao","doi":"10.1088/1361-6420/ad7055","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7055","url":null,"abstract":"This paper investigates inverse source problems for the Helmholtz and Navier equations in multi-layered media, considering both two and three-dimensional cases respectively. The study reveals a consistent increase in stability for each scenario, characterized by two main terms: a Hölder-type term associated with data discrepancy, and a logarithmic-type term that diminishes as more frequencies are considered. In the two-dimensional case, measurements on interfaces and far-field data are essential. By employing the fundamental solution in free-space as the test function and utilizing the asymptotic behavior of the solution and continuation principle, stability results are obtained. In the three-dimensional case, measurements on interfaces and artificial boundaries are taken, and the stability result can be derived by applying the arguments for inverse source problems in homogeneous media.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210300","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
Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary 具有导电边界的各向异性散射体的单调性方法分析
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-27 DOI: 10.1088/1361-6420/ad7053
Isaac Harris, Victor Hughes, Heejin Lee
{"title":"Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary","authors":"Isaac Harris, Victor Hughes, Heejin Lee","doi":"10.1088/1361-6420/ad7053","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7053","url":null,"abstract":"In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far–field pattern is known/measured and we consider two inverse problems. First, we show that the far–field data uniquely determines the boundary coefficient. Next, since it is known that anisotropic coefficients are not uniquely determined by this data we will develop a qualitative method to recover the scatterer. To this end, we study the so–called monotonicity method applied to this inverse shape problem. This method has recently been applied to some inverse scattering problems but this is the first time it has been applied to an anisotropic scatterer. This method allows one to recover the scatterer by considering the eigenvalues of an operator associated with the far–field operator. We present some simple numerical reconstructions to illustrate our theory in two dimensions. For our reconstructions, we need to compute the adjoint of the Herglotz wave function as an operator mapping into <italic toggle=\"yes\">H</italic><sup>1</sup> of a small ball.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"21 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226720","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
Bayesian image segmentation under varying blur with triplet Markov random field 利用三重马尔可夫随机场在不同模糊条件下进行贝叶斯图像分割
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-08-14 DOI: 10.1088/1361-6420/ad6a34
Sonia Ouali, Jean-Baptiste Courbot, Romain Pierron, Olivier Haeberlé
{"title":"Bayesian image segmentation under varying blur with triplet Markov random field","authors":"Sonia Ouali, Jean-Baptiste Courbot, Romain Pierron, Olivier Haeberlé","doi":"10.1088/1361-6420/ad6a34","DOIUrl":"https://doi.org/10.1088/1361-6420/ad6a34","url":null,"abstract":"In this paper, we place ourselves in the context of the Bayesian framework for image segmentation in the presence of varying blur. The proposed approach is based on Triplet Markov Random Fields (TMRF). This method takes into account, during segmentation, peculiarities of an image such as noise, blur, and texture. We present an unsupervised TMRF method, which jointly deals with the problem of segmentation, and that of depth estimation in order to process fluorescence microscopy images. In addition to the estimation of the depth maps using the Metropolis-Hasting and the Stochastic Parameter Estimation (SPE) algorithms, we also estimate the model parameters using the SPE algorithm. We compare our TMRF method to other MRF models on simulated images, and to an unsupervised method from the state of art on real fluorescence microscopy images. Our method offers improved results, especially when blur is important.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"177 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210301","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
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