Inverse Problems最新文献

{"title":"Quantifying predictive uncertainty in damage classification for Nondestructive Evaluation using Bayesian approximation and deep learning","authors":"Zi Li, Yiming Deng","doi":"10.1088/1361-6420/ad2f63","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2f63","url":null,"abstract":"\u0000 Magnetic flux leakage (MFL), a widely used Nondestructive Evaluation (NDE) method, for inspecting pipelines to prevent potential long-term failures. During field testing, uncertainties can affect the accuracy of the inspection and the decision-making process regarding damage conditions. Therefore, it is essential to identify and quantify these uncertainties to ensure the reliability of the inspection. This study focuses on the uncertainties that arise during the inverse NDE process due to the dynamic magnetization process, which is affected by the relative motion of the MFL sensor and the material being tested. Specifically, the study investigates the uncertainties caused by sensing liftoff, which can affect the output signal of the sensing system. Due to the complexity of describing the forward uncertainty propagation process, this study compared two typical machine learning-based approximate Bayesian inference methods, Convolutional Neural Network (CNN) and Deep Ensemble (DE), to address the input uncertainty from the MFL response data. Besides, an Autoencoder method is applied to tackle the lack of experimental data for the training model by augmenting the dataset, which is constructed with the pre-trained model based on transfer learning. Prior knowledge learned from large simulated MFL signals can fine-tune the Autoencoder model which enhances the subsequent learning process on experimental MFL data with faster generalization. The augmented data from the fine-tuned Autoencoder is further applied for machine learning-based defect size classification. This study conducted prediction accuracy and uncertainty analysis with calibration, which can evaluate the prediction performance and reveal the relation between the liftoff uncertainty and prediction accuracy. Further, to strengthen the trustworthiness of the prediction results, the decision-making process guided by uncertainty is applied to provide valuable insights into the reliability of the final prediction results. Overall, the proposed framework for uncertainty quantification offers valuable insights into the assessment of reliability in MFL-based decision-making and inverse problems.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"32 40","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140081518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reconstruction of averaging indicators for highly heterogeneous media","authors":"Lorenzo Audibert, H. Haddar, Fabien Pourre","doi":"10.1088/1361-6420/ad2f64","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2f64","url":null,"abstract":"\u0000 We propose a new imaging algorithm capable of producing quantitative indicator functions for unknown and possibly highly oscillating media from multistatic far field measurements of scattered fields at a fixed frequency. The algorithm exploits the notion of modified transmission eigenvalues and their determination from measurements. We propose in particular the use of a new modified background obtained as the limit of a metamaterial background. It has the specificity of having a unique non trivial eigenvalue, which is particularly suited for the proposed imaging procedure. We show the efficiency of this new algorithm on some 2D experiments and emphasize its superiority with respect to some clasical approaches such as the Linear Sampling Method.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"53 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140082211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microwave time reversal for nondestructive testing of buried small damage in composite materials","authors":"Kang An, Changyou Li, Guoqian Long, Jun Ding","doi":"10.1088/1361-6420/ad2902","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2902","url":null,"abstract":"\u0000 Composite materials are widely applied in aerospace, civil engineering, and sports equipment. Various damages produced during fabrication and long-term use can destroy its original mechanical properties, which brings safety and structural healthy concerns. Microwave imaging based on time reversal is one of the most promising nondestructive testing (NDT) methods for portable, low-cost, and accurate testing with the advantages of auto-focus and super-resolution. This paper applied microwave time reversal for the detection of buried small damage in composites backed by metal plates. Strong reflection from composite-metal interfaces brings challenges in successfully achieving time-reversal auto-focusing on small and weak-scattering damages in composites. Traditional target localization methods, including the entropy regularization method (ERM) and time-integrated energy method (TIEM), may result in the wrong localization of small damages. The main contribution of this paper is that the localization problem caused by the strong reflection from metal plates is revealed first, and the target initial reflection method (TIRM) from through-wall-radar imaging is introduced to solve it. The performance of three target localization methods is investigated, and the physical reasons for failure or successful localization are discussed in detail. Some performance influence factors, such as the arrangement of receivers or the total time step of received signals, are also discussed. Good performance for the detection of a single small damage with a weak scattered signal is achieved, and the performance for detecting multiple damages is studied. All time-reversal simulations are carried out based on the finite-difference time-domain (FDTD) method.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"98 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139839766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient kernel canonical correlation analysis using Nyström approximation","authors":"Qin Fang, Lei Shi, Min Xu, Ding-Xuan Zhou","doi":"10.1088/1361-6420/ad2900","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2900","url":null,"abstract":"\u0000 The main contribution of this paper is the derivation of non-asymptotic convergence rates for Nystr\"om kernel CCA in a setting of statistical learning. Our theoretical results reveal that, under certain conditions, Nystr\"om kernel CCA can achieve a convergence rate comparable to that of the standard kernel CCA, while offering significant computational savings. This finding has important implications for the practical application of kernel CCA, particularly in scenarios where computational efficiency is crucial. Numerical experiments are provided to demonstrate the effectiveness of Nystr\"om kernel CCA.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"65 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139841334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microwave time reversal for nondestructive testing of buried small damage in composite materials","authors":"Kang An, Changyou Li, Guoqian Long, Jun Ding","doi":"10.1088/1361-6420/ad2902","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2902","url":null,"abstract":"\u0000 Composite materials are widely applied in aerospace, civil engineering, and sports equipment. Various damages produced during fabrication and long-term use can destroy its original mechanical properties, which brings safety and structural healthy concerns. Microwave imaging based on time reversal is one of the most promising nondestructive testing (NDT) methods for portable, low-cost, and accurate testing with the advantages of auto-focus and super-resolution. This paper applied microwave time reversal for the detection of buried small damage in composites backed by metal plates. Strong reflection from composite-metal interfaces brings challenges in successfully achieving time-reversal auto-focusing on small and weak-scattering damages in composites. Traditional target localization methods, including the entropy regularization method (ERM) and time-integrated energy method (TIEM), may result in the wrong localization of small damages. The main contribution of this paper is that the localization problem caused by the strong reflection from metal plates is revealed first, and the target initial reflection method (TIRM) from through-wall-radar imaging is introduced to solve it. The performance of three target localization methods is investigated, and the physical reasons for failure or successful localization are discussed in detail. Some performance influence factors, such as the arrangement of receivers or the total time step of received signals, are also discussed. Good performance for the detection of a single small damage with a weak scattered signal is achieved, and the performance for detecting multiple damages is studied. All time-reversal simulations are carried out based on the finite-difference time-domain (FDTD) method.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"63 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139779886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of the Born data in inverse scattering of layered media","authors":"Zekui Jia, Maokun Li, Fan Yang, Shenheng Xu","doi":"10.1088/1361-6420/ad2903","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2903","url":null,"abstract":"\u0000 The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output (MIMO) data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulted Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"143 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139780601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of the Born data in inverse scattering of layered media","authors":"Zekui Jia, Maokun Li, Fan Yang, Shenheng Xu","doi":"10.1088/1361-6420/ad2903","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2903","url":null,"abstract":"\u0000 The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output (MIMO) data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulted Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"38 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139840242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient kernel canonical correlation analysis using Nyström approximation","authors":"Qin Fang, Lei Shi, Min Xu, Ding-Xuan Zhou","doi":"10.1088/1361-6420/ad2900","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2900","url":null,"abstract":"\u0000 The main contribution of this paper is the derivation of non-asymptotic convergence rates for Nystr\"om kernel CCA in a setting of statistical learning. Our theoretical results reveal that, under certain conditions, Nystr\"om kernel CCA can achieve a convergence rate comparable to that of the standard kernel CCA, while offering significant computational savings. This finding has important implications for the practical application of kernel CCA, particularly in scenarios where computational efficiency is crucial. Numerical experiments are provided to demonstrate the effectiveness of Nystr\"om kernel CCA.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"95 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139781329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Image reconstruction based on nonlinear diffusion model for limited-angle computed tomography","authors":"Xuying Zhao, Wenjin Jiang, Xinting Zhang, Wenxiu Guo, Yunsong Zhao, Xing Zhao","doi":"10.1088/1361-6420/ad2695","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2695","url":null,"abstract":"\u0000 The problem of limited-angle computed tomography (CT) imaging reconstruction has a wide range of practical applications. Due to various factors such as high X-ray absorption, structural characteristics of the scanned object, and equipment limitations, it is often impractical to obtain a complete angular scan, resulting in limited-angle scan data. In this paper, we propose an iterative image reconstruction algorithm for limited-angle CT. The algorithm carries out a traditional CT reconstruction and a nonlinear diffusion process alternatively. Specifically, a subtle partial differ ential equation (PDE) is constructed to guide the nonlinear diffusion process to eliminate limited angle artifacts in the reconstructed image. Numerical experiments on both analytic data and real data validate the efficacy of the proposed nonlinear diffusion reconstruction (NDR) algorithm. Furthermore, a linear diffusion reconstruction (LDR) algorithm which combines a traditional CT re construction algorithm and a linear diffusion process is also presented in the paper.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"6 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139861043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Image reconstruction based on nonlinear diffusion model for limited-angle computed tomography","authors":"Xuying Zhao, Wenjin Jiang, Xinting Zhang, Wenxiu Guo, Yunsong Zhao, Xing Zhao","doi":"10.1088/1361-6420/ad2695","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2695","url":null,"abstract":"\u0000 The problem of limited-angle computed tomography (CT) imaging reconstruction has a wide range of practical applications. Due to various factors such as high X-ray absorption, structural characteristics of the scanned object, and equipment limitations, it is often impractical to obtain a complete angular scan, resulting in limited-angle scan data. In this paper, we propose an iterative image reconstruction algorithm for limited-angle CT. The algorithm carries out a traditional CT reconstruction and a nonlinear diffusion process alternatively. Specifically, a subtle partial differ ential equation (PDE) is constructed to guide the nonlinear diffusion process to eliminate limited angle artifacts in the reconstructed image. Numerical experiments on both analytic data and real data validate the efficacy of the proposed nonlinear diffusion reconstruction (NDR) algorithm. Furthermore, a linear diffusion reconstruction (LDR) algorithm which combines a traditional CT re construction algorithm and a linear diffusion process is also presented in the paper.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139801179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}