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A microlocal and visual comparison of 2D Kirchhoff migration formulas in seismic imaging * 地震成像中二维基尔霍夫迁移公式的微观和视觉比较 *
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-18 DOI: 10.1088/1361-6420/ad797b
Kevin Ganster, Eric Todd Quinto and Andreas Rieder
{"title":"A microlocal and visual comparison of 2D Kirchhoff migration formulas in seismic imaging *","authors":"Kevin Ganster, Eric Todd Quinto and Andreas Rieder","doi":"10.1088/1361-6420/ad797b","DOIUrl":"https://doi.org/10.1088/1361-6420/ad797b","url":null,"abstract":"The term Kirchhoff migration refers to a collection of approximate linearized inversion formulas for solving the inverse problem of seismic tomography which entails reconstructing the Earth’s subsurface from reflected wave fields. A number of such formulas exists, the first dating from the 1950 s. As far as we know, these formulas have not yet been mathematically compared with respect to their imaging properties. This shortcoming is to be alleviated by the present work: we systematically discuss the advantages and disadvantages of the formulas in 2D from a microlocal point of view. To this end we consider the corresponding imaging operators in an unified framework as pseudodifferential or Fourier integral operators. Numerical examples illustrate the theoretical insights and allow a visual comparison of the different formulas.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258276","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
Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs 具有两个考奇数据对的反导问题的 Lipschitz 稳定性
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-12 DOI: 10.1088/1361-6420/ad76d4
Martin Hanke
{"title":"Lipschitz stability of an inverse conductivity problem with two Cauchy data pairs","authors":"Martin Hanke","doi":"10.1088/1361-6420/ad76d4","DOIUrl":"https://doi.org/10.1088/1361-6420/ad76d4","url":null,"abstract":"In 1996 Seo proved that two appropriate pairs of current and voltage data measured on the surface of a planar homogeneous object are sufficient to determine a conductive polygonal inclusion with known deviating conductivity. Here we show that the corresponding linearized forward map is injective, and from this we deduce Lipschitz stability of the solution of the original nonlinear inverse problem. We also treat the case of an insulating polygonal inclusion, in which case a single pair of Cauchy data is already sufficient for the same purpose.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210256","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 bilevel optimization method for inverse mean-field games * 逆均值场博弈的双层优化方法 *
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-12 DOI: 10.1088/1361-6420/ad75b0
Jiajia Yu, Quan Xiao, Tianyi Chen and Rongjie Lai
{"title":"A bilevel optimization method for inverse mean-field games *","authors":"Jiajia Yu, Quan Xiao, Tianyi Chen and Rongjie Lai","doi":"10.1088/1361-6420/ad75b0","DOIUrl":"https://doi.org/10.1088/1361-6420/ad75b0","url":null,"abstract":"In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in maintaining the convexity of the objective function and the linearity of constraints in the forward problem. Our paper focuses on inverse mean-field games characterized by unknown obstacles and metrics. We show numerical stability for these two types of inverse problems. More importantly, we, for the first time, establish the identifiability of the inverse mean-field game with unknown obstacles via the solution of the resultant bilevel problem. The bilevel approach enables us to employ an alternating gradient-based optimization algorithm with a provable convergence guarantee. To validate the effectiveness of our methods in solving the inverse problems, we have designed comprehensive numerical experiments, providing empirical evidence of its efficacy.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210255","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 inversion with Student’s t priors based on Gaussian scale mixtures 基于高斯尺度混合物的贝叶斯反演与学生 t 先验
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-11 DOI: 10.1088/1361-6420/ad75af
Angelina Senchukova, Felipe Uribe and Lassi Roininen
{"title":"Bayesian inversion with Student’s t priors based on Gaussian scale mixtures","authors":"Angelina Senchukova, Felipe Uribe and Lassi Roininen","doi":"10.1088/1361-6420/ad75af","DOIUrl":"https://doi.org/10.1088/1361-6420/ad75af","url":null,"abstract":"Many inverse problems focus on recovering a quantity of interest that is a priori known to exhibit either discontinuous or smooth behavior. Within the Bayesian approach to inverse problems, such structural information can be encoded using Markov random field priors. We propose a class of priors that combine Markov random field structure with Student’s t distribution. This approach offers flexibility in modeling diverse structural behaviors depending on available data. Flexibility is achieved by including the degrees of freedom parameter of Student’s t distribution in the formulation of the Bayesian inverse problem. To facilitate posterior computations, we employ Gaussian scale mixture representation for the Student’s t Markov random field prior, which allows expressing the prior as a conditionally Gaussian distribution depending on auxiliary hyperparameters. Adopting this representation, we can derive most of the posterior conditional distributions in a closed form and utilize the Gibbs sampler to explore the posterior. We illustrate the method with two numerical examples: signal deconvolution and image deblurring.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210297","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
Exact recovery of the support of piecewise constant images via total variation regularization 通过总变异正则化精确恢复片断常数图像的支持度
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-11 DOI: 10.1088/1361-6420/ad75b1
Yohann De Castro, Vincent Duval and Romain Petit
{"title":"Exact recovery of the support of piecewise constant images via total variation regularization","authors":"Yohann De Castro, Vincent Duval and Romain Petit","doi":"10.1088/1361-6420/ad75b1","DOIUrl":"https://doi.org/10.1088/1361-6420/ad75b1","url":null,"abstract":"This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show that, if the unknown image is the superposition of a few simple shapes, and if a non-degenerate source condition holds, then, in the low noise regime, the reconstructed images have the same structure: they are the superposition of the same number of shapes, each a smooth deformation of one of the unknown shapes. Moreover, the reconstructed shapes and the associated intensities converge to the unknown ones as the noise goes to zero.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210287","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
fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data fg-ORKA：多维数据中移动和变形物体的快速无网格重建
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-11 DOI: 10.1088/1361-6420/ad7495
Florian Bossmann, Jianwei Ma and Wenze Wu
{"title":"fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data","authors":"Florian Bossmann, Jianwei Ma and Wenze Wu","doi":"10.1088/1361-6420/ad7495","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7495","url":null,"abstract":"Identifying and tracking objects over multiple observations is a frequent task in many applications. Traffic monitoring requires the tracking of vehicles or pedestrians in video data and geophysical exploration relies on identifying seismic wave fronts from data of multiple sensors, only to mention two examples. In many cases, the object changes its shape or position within the given data from one observation to another. Vehicles can change their position and angle relative to the camera while seismic waves have different arrival times, frequencies, or intensities depending on the sensor position. This complicates the task at hand. In a previous work, the authors presented a new algorithm to solve this problem—object reconstruction using K-approximation (ORKA). This algorithm is hindered by two conflicting limitations: the tracked movement is limited by the sampling grid while the complexity increases exponentially with the resolution. We introduce an iterative variant of the ORKA algorithm that is able to overcome this conflict. We also give a brief introduction on the original ORKA algorithm. Knowledge of the previous work is thus not required. We give theoretical error bounds and a complexity analysis which we validate with several numerical experiments. Moreover, we discuss the influence of different parameter choices in detail. The results clearly show that the iterative approach can outperform ORKA in both accuracy and efficiency. On the example of video processing we show that the new method can be applied where the original algorithm is too time and memory intensive. Furthermore, we demonstrate on seismic exploration data that we are now able to recover much finer details on the wave front movement then before.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210289","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
Reconstructing a state-independent cost function in a mean-field game model 重构均值场博弈模型中与状态无关的成本函数
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-05 DOI: 10.1088/1361-6420/ad7497
Kui Ren, Nathan Soedjak, Kewei Wang, Hongyu Zhai
{"title":"Reconstructing a state-independent cost function in a mean-field game model","authors":"Kui Ren, Nathan Soedjak, Kewei Wang, Hongyu Zhai","doi":"10.1088/1361-6420/ad7497","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7497","url":null,"abstract":"In this short note, we consider an inverse problem to a mean-field games (MFGs) system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a uniqueness result for the inverse problem using the standard multilinearization technique. One of the main features of our work is that we insist that the population distribution be a probability measure, a requirement that is not enforced in some of the existing literature on theoretical inverse MFGs.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210288","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
Bouligand–Newton type methods for non-smooth ill-posed problems 非光滑问题的布利甘-牛顿型方法
IF 2.1 2区 数学
Inverse Problems Pub Date : 2024-09-05 DOI: 10.1088/1361-6420/ad7496
Qinian Jin, Yun Zhang
{"title":"Bouligand–Newton type methods for non-smooth ill-posed problems","authors":"Qinian Jin, Yun Zhang","doi":"10.1088/1361-6420/ad7496","DOIUrl":"https://doi.org/10.1088/1361-6420/ad7496","url":null,"abstract":"We consider Newton-type methods for solving nonlinear ill-posed inverse problems in Hilbert spaces where the forward operators are not necessarily Gâteaux differentiable. Modifications are proposed with the non-existing Fréchet derivatives replaced by a family of bounded linear operators satisfying suitable properties. These bounded linear operators can be constructed by the Bouligand subderivatives which are defined as limits of Fréchet derivatives of the forward operator in differentiable points. The Bouligand subderivative mapping in general is not continuous unless the forward operator is Gâteaux differentiable which introduces challenges for convergence analysis of the corresponding Bouligand–Newton type methods. In this paper we will show that, under the discrepancy principle, these Bouligand–Newton type methods are iterative regularization methods of optimal order. Numerical results for an inverse problem arising from a non-smooth semi-linear elliptic equation are presented to test the performance of the methods.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226723","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
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":null,"pages":null},"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":null,"pages":null},"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
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