Inverse Problems最新文献_第9页

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

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-05 DOI: 10.1088/1361-6420/ad2901

Sarah Eberle-Blick, Valter Pohjola

引用次数: 0

MiPhDUO: microwave imaging via physics-informed deep unrolled optimization MiPhDUO：通过物理信息深度展开优化进行微波成像

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-04 DOI: 10.1088/1361-6420/ad2b99

Sabrina Zumbo, Stefano Mandija, Tommaso Isernia, Martina T Bevacqua

{"title":"MiPhDUO: microwave imaging via physics-informed deep unrolled optimization","authors":"Sabrina Zumbo, Stefano Mandija, Tommaso Isernia, Martina T Bevacqua","doi":"10.1088/1361-6420/ad2b99","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2b99","url":null,"abstract":"Microwave imaging (MWI) is a non-invasive technique that can identify unknown scatterer objects’ features while offering advantages such as low cost and portable devices with respect to other imaging methods. However, MWI faces challenges in solving the underlying inverse scattering problem, which involves recovering target properties from its scattered fields. Existing methods include linearized and non-linear optimization approaches, but they have limitations respectively in terms of range of validity and computational complexity (in view of the possible occurrence of ‘false solutions’). In recent years, learning-based approaches have emerged as they can allow real-time imaging but usually lack generalizability and a direct connection to the underlying physics. This paper proposes a physics-informed approach that combines convolutional neural networks with physics-based calculations. It is based on a few cascaded operations, making use of the gradient of the relevant cost function, and successively improving the estimation of the unknown target. The proposed approach is assessed using simulated as well as experimental Fresnel data. The results show that the integration of physics with deep learning can contribute to improve reconstruction accuracy, generalizability, and computational efficiency in MWI.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315434","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

CUQIpy: II. Computational uncertainty quantification for PDE-based inverse problems in Python CUQIpy：II.用 Python 对基于 PDE 的逆问题进行计算不确定性量化

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-04 DOI: 10.1088/1361-6420/ad22e8

Amal M A Alghamdi, Nicolai A B Riis, Babak M Afkham, Felipe Uribe, Silja L Christensen, Per Christian Hansen, Jakob S Jørgensen

{"title":"CUQIpy: II. Computational uncertainty quantification for PDE-based inverse problems in Python","authors":"Amal M A Alghamdi, Nicolai A B Riis, Babak M Afkham, Felipe Uribe, Silja L Christensen, Per Christian Hansen, Jakob S Jørgensen","doi":"10.1088/1361-6420/ad22e8","DOIUrl":"https://doi.org/10.1088/1361-6420/ad22e8","url":null,"abstract":"Inverse problems, particularly those governed by Partial Differential Equations (PDEs), are prevalent in various scientific and engineering applications, and uncertainty quantification (UQ) of solutions to these problems is essential for informed decision-making. This second part of a two-paper series builds upon the foundation set by the first part, which introduced <sans-serif>CUQIpy</sans-serif>, a Python software package for computational UQ in inverse problems using a Bayesian framework. In this paper, we extend <sans-serif>CUQIpy</sans-serif>’s capabilities to solve PDE-based Bayesian inverse problems through a general framework that allows the integration of PDEs in <sans-serif>CUQIpy</sans-serif>, whether expressed natively or using third-party libraries such as <sans-serif>FEniCS</sans-serif>. <sans-serif>CUQIpy</sans-serif> offers concise syntax that closely matches mathematical expressions, streamlining the modeling process and enhancing the user experience. The versatility and applicability of <sans-serif>CUQIpy</sans-serif> to PDE-based Bayesian inverse problems are demonstrated on examples covering parabolic, elliptic and hyperbolic PDEs. This includes problems involving the heat and Poisson equations and application case studies in electrical impedance tomography and photo-acoustic tomography, showcasing the software’s efficiency, consistency, and intuitive interface. This comprehensive approach to UQ in PDE-based inverse problems provides accessibility for non-experts and advanced features for experts.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315294","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

CUQIpy: I. Computational uncertainty quantification for inverse problems in Python CUQIpy：I. 用 Python 计算逆问题的不确定性量化

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-04 DOI: 10.1088/1361-6420/ad22e7

Nicolai A B Riis, Amal M A Alghamdi, Felipe Uribe, Silja L Christensen, Babak M Afkham, Per Christian Hansen, Jakob S Jørgensen

{"title":"CUQIpy: I. Computational uncertainty quantification for inverse problems in Python","authors":"Nicolai A B Riis, Amal M A Alghamdi, Felipe Uribe, Silja L Christensen, Babak M Afkham, Per Christian Hansen, Jakob S Jørgensen","doi":"10.1088/1361-6420/ad22e7","DOIUrl":"https://doi.org/10.1088/1361-6420/ad22e7","url":null,"abstract":"This paper introduces <sans-serif>CUQIpy</sans-serif>, a versatile open-source Python package for computational uncertainty quantification (UQ) in inverse problems, presented as Part I of a two-part series. <sans-serif>CUQIpy</sans-serif> employs a Bayesian framework, integrating prior knowledge with observed data to produce posterior probability distributions that characterize the uncertainty in computed solutions to inverse problems. The package offers a high-level modeling framework with concise syntax, allowing users to easily specify their inverse problems, prior information, and statistical assumptions. <sans-serif>CUQIpy</sans-serif> supports a range of efficient sampling strategies and is designed to handle large-scale problems. Notably, the automatic sampler selection feature analyzes the problem structure and chooses a suitable sampler without user intervention, streamlining the process. With a selection of probability distributions, test problems, computational methods, and visualization tools, <sans-serif>CUQIpy</sans-serif> serves as a powerful, flexible, and adaptable tool for UQ in a wide selection of inverse problems. Part II of the series focuses on the use of <sans-serif>CUQIpy</sans-serif> for UQ in inverse problems with partial differential equations.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315436","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

Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors 利用稀疏边界数据和动态传感器恢复不连续热方程源

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-01 DOI: 10.1088/1361-6420/ad2904

Guang Lin, Na Ou, Zecheng Zhang, Zhidong Zhang

引用次数: 0

Quantitative passive imaging by iterative holography: the example of helioseismic holography 通过迭代全息技术进行定量被动成像：日震全息技术实例

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-01 DOI: 10.1088/1361-6420/ad2b9a

Björn Müller, Thorsten Hohage, Damien Fournier, Laurent Gizon

{"title":"Quantitative passive imaging by iterative holography: the example of helioseismic holography","authors":"Björn Müller, Thorsten Hohage, Damien Fournier, Laurent Gizon","doi":"10.1088/1361-6420/ad2b9a","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2b9a","url":null,"abstract":"In passive imaging, one attempts to reconstruct some coefficients in a wave equation from correlations of observed randomly excited solutions to this wave equation. Many methods proposed for this class of inverse problem so far are only qualitative, e.g. trying to identify the support of a perturbation. Major challenges are the increase in dimensionality when computing correlations from primary data in a preprocessing step, and often very poor pointwise signal-to-noise ratios. In this paper, we propose an approach that addresses both of these challenges: it works only on the primary data while implicitly using the full information contained in the correlation data, and it provides quantitative estimates and convergence by iteration. Our work is motivated by helioseismic holography, a well-established imaging method to map heterogenities and flows in the solar interior. We show that the back-propagation used in classical helioseismic holography can be interpreted as the adjoint of the Fréchet derivative of the operator which maps the properties of the solar interior to the correlation data on the solar surface. The theoretical and numerical framework for passive imaging problems developed in this paper extends helioseismic holography to nonlinear problems and allows for quantitative reconstructions. We present a proof of concept in uniform media.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315430","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 a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds 横向各向异性流形上非线性薛定谔方程线性化反边界值问题的稳定性增强

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-23 DOI: 10.1088/1361-6420/ad2533

Shuai Lu, Jian Zhai

引用次数: 0