Inverse Problems最新文献_第8页

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":"51 1","pages":""},"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":"23 1","pages":""},"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":"140 1","pages":""},"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":"33 1","pages":""},"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

Adaptive anisotropic Bayesian meshing for inverse problems 逆问题的自适应各向异性贝叶斯网格划分

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-23 DOI: 10.1088/1361-6420/ad2696

A Bocchinfuso, D Calvetti, E Somersalo

{"title":"Adaptive anisotropic Bayesian meshing for inverse problems","authors":"A Bocchinfuso, D Calvetti, E Somersalo","doi":"10.1088/1361-6420/ad2696","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2696","url":null,"abstract":"We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that errors arising from the discretization can be detrimental for ill-posed inverse problems, as discretization error behaves as correlated noise. While this problem can be avoided with a discretization fine enough to decrease the modeling error level below that of the exogenous noise that is addressed, e.g. by regularization, the computational resources needed to deal with the additional degrees of freedom may increase so much as to require high performance computing environments. Following an earlier idea, we advocate the notion of the discretization as one of the unknowns of the inverse problem, which is updated iteratively together with the solution. In this approach, the discretization, defined in terms of an underlying metric, is refined selectively only where the representation power of the current mesh is insufficient. In this paper we allow the metrics and meshes to be anisotropic, and we show that this leads to significant reduction of memory allocation and computing time.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"174 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004917","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 Bayesian approach for consistent reconstruction of inclusions 用贝叶斯方法重建内含物的一致性

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-23 DOI: 10.1088/1361-6420/ad2531

B M Afkham, K Knudsen, A K Rasmussen, T Tarvainen

引用次数: 0

Imaging of nonlinear materials via the Monotonicity Principle 通过单调性原理成像非线性材料

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-13 DOI: 10.1088/1361-6420/ad22e9

Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli, Antonello Tamburrino

{"title":"Imaging of nonlinear materials via the Monotonicity Principle","authors":"Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli, Antonello Tamburrino","doi":"10.1088/1361-6420/ad22e9","DOIUrl":"https://doi.org/10.1088/1361-6420/ad22e9","url":null,"abstract":"Inverse problems, which are related to Maxwell’s equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such problems pose. Retrieving the spatial behavior of some unknown physical property, from boundary measurements, is a nonlinear and highly ill-posed problem even in the presence of linear materials. Furthermore, this complexity grows exponentially in the presence of nonlinear materials. In the tomography of linear materials, the Monotonicity Principle (MP) is the foundation of a class of non-iterative algorithms able to guarantee excellent performances and compatibility with real-time applications. Recently, the MP has been extended to nonlinear materials under very general assumptions. Starting from the theoretical background for this extension, we develop a first real-time inversion method for the inverse obstacle problem in the presence of nonlinear materials. The proposed method is intendend for all problems governed by the quasilinear Laplace equation, i.e. static problems involving nonlinear materials. In this paper, we provide some preliminary results which give the foundation of our method and some extended numerical examples.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004658","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

Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems 用于大规模逆问题的多层次维度独立似然信息 MCMC

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-05 DOI: 10.1088/1361-6420/ad1e2c

Tiangang Cui, Gianluca Detommaso, Robert Scheichl

{"title":"Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems","authors":"Tiangang Cui, Gianluca Detommaso, Robert Scheichl","doi":"10.1088/1361-6420/ad1e2c","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1e2c","url":null,"abstract":"We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui <italic toggle=\"yes\">et al</italic> 2016) and the multilevel MCMC (Dodwell <italic toggle=\"yes\">et al</italic> 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic <italic toggle=\"yes\">likelihood-informed subspace</italic> (LIS) (Cui <italic toggle=\"yes\">et al</italic> 2014)—which involves a number of forward and adjoint model simulations—to design accelerated operator-weighted proposals. By exploiting the multilevel structure of the discretised parameters and discretised forward models, we design a <italic toggle=\"yes\">Rayleigh–Ritz procedure</italic> to significantly reduce the computational effort in building the LIS and operating with DILI proposals. Second, the resulting DILI-MCMC can drastically improve the sampling efficiency of MCMC at each level, and hence reduce the integration error of the multilevel algorithm for fixed CPU time. Numerical results confirm the improved computational efficiency of the multilevel DILI approach.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"69 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762540","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