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Inverse Problems and Imaging最新文献

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Inverse obstacle scattering for acoustic waves in the time domain 声波在时域上的逆障碍物散射
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021037
Lu Zhao, Heping Dong, Fuming Ma
{"title":"Inverse obstacle scattering for acoustic waves in the time domain","authors":"Lu Zhao, Heping Dong, Fuming Ma","doi":"10.3934/IPI.2021037","DOIUrl":"https://doi.org/10.3934/IPI.2021037","url":null,"abstract":"This paper concerns an inverse acoustic scattering problem which is to determine the location and shape of a rigid obstacle from time domain scattered field data. An efficient convolution quadrature method combined with nonlinear integral equation method is proposed to solve the inverse problem. In particular, replacing the classic Fourier transform with the convolution quadrature method for time discretization, the boundary integral equations for the Helmholtz equation with complex wave numbers can be obtained to guarantee the numerically approximate causality property of the scattered field under some condition. Numerical experiments are presented to demonstrate the effectiveness and robustness of the proposed method.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80057284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Limited-angle CT reconstruction with generalized shrinkage operators as regularizers 以广义收缩算子为正则化算子的有限角度CT重构
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021019
Xiaojuan Deng, Xing Zhao, Mengfei Li, Hongwei Li
{"title":"Limited-angle CT reconstruction with generalized shrinkage operators as regularizers","authors":"Xiaojuan Deng, Xing Zhao, Mengfei Li, Hongwei Li","doi":"10.3934/IPI.2021019","DOIUrl":"https://doi.org/10.3934/IPI.2021019","url":null,"abstract":"Limited-angle reconstruction is a very important but challenging problem in the field of computed tomography (CT) which has been extensively studied for many years. However, some difficulties still remain. Based on the theory of visible and invisible boundary developed by Quinto et.al, we propose a reconstruction model for limited-angle CT, which encodes the visible edges as priors to recover the invisible ones. The new model utilizes generalized shrinkage operators as regularizers to perform edge-preserving smoothing such that the visible edges are employed as anchors to recover piecewise-constant or piecewise-smooth reconstructions, while noises and artifacts are suppressed or removed. This work extends our previous research on limited-angle reconstruction which employs gradient begin{document}$ ell_0 $end{document} and begin{document}$ ell_1 $end{document} norm regularizers. The effectiveness of the proposed model and its corresponding solving algorithm shall be verified by numerical experiments with simulated data as well as real data.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77647198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
A new initialization method based on normed statistical spaces in deep networks 一种基于归一统计空间的深度网络初始化方法
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2020045
Hongfei Yang, Xiaofeng Ding, R. Chan, Huai-Bin Hui, Yaxin Peng, T. Zeng
{"title":"A new initialization method based on normed statistical spaces in deep networks","authors":"Hongfei Yang, Xiaofeng Ding, R. Chan, Huai-Bin Hui, Yaxin Peng, T. Zeng","doi":"10.3934/ipi.2020045","DOIUrl":"https://doi.org/10.3934/ipi.2020045","url":null,"abstract":"Training deep neural networks can be difficult. For classical neural networks, the initialization method by Xavier and Yoshua which is later generalized by He, Zhang, Ren and Sun can facilitate stable training. However, with the recent development of new layer types, we find that the above mentioned initialization methods may fail to lead to successful training. Based on these two methods, we will propose a new initialization by studying the parameter space of a network. Our principal is to put constrains on the growth of parameters in different layers in a consistent way. In order to do so, we introduce a norm to the parameter space and use this norm to measure the growth of parameters. Our new method is suitable for a wide range of layer types, especially for layers with parameter-sharing weight matrices.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89973276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
A variational saturation-value model for image decomposition: Illumination and reflectance 图像分解的变分饱和值模型:光照和反射率
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021061
Wei Wang, Caifei Li
{"title":"A variational saturation-value model for image decomposition: Illumination and reflectance","authors":"Wei Wang, Caifei Li","doi":"10.3934/ipi.2021061","DOIUrl":"https://doi.org/10.3934/ipi.2021061","url":null,"abstract":"In this paper, we study to decompose a color image into the illumination and reflectance components in saturation-value color space. By considering the spatial smoothness of the illumination component, the total variation regularization of the reflectance component, and the data-fitting in saturation-value color space, we develop a novel variational saturation-value model for image decomposition. The main aim of the proposed model is to formulate the decomposition of a color image such that the illumination component is uniform with only brightness information, and the reflectance component contains the color information. We establish the theoretical result about the existence of the solution of the proposed minimization problem. We employ a primal-dual algorithm to solve the proposed minimization problem. Experimental results are shown to illustrate the effectiveness of the proposed decomposition model in saturation-value color space, and demonstrate the performance of the proposed method is better than the other testing methods.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77064667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Euler equations and trace properties of minimizers of a functional for motion compensated inpainting 欧拉方程及运动补偿中泛函最小值的迹线性质
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021072
R. March, G. Riey
{"title":"Euler equations and trace properties of minimizers of a functional for motion compensated inpainting","authors":"R. March, G. Riey","doi":"10.3934/ipi.2021072","DOIUrl":"https://doi.org/10.3934/ipi.2021072","url":null,"abstract":"<p style='text-indent:20px;'>We compute the Euler equations of a functional useful for simultaneous video inpainting and motion estimation, which was obtained in [<xref ref-type=\"bibr\" rid=\"b17\">17</xref>] as the relaxation of a modified version of the functional proposed in [<xref ref-type=\"bibr\" rid=\"b16\">16</xref>]. The functional is defined on vectorial functions of bounded variations, therefore we also get the Euler equations holding on the singular sets of minimizers, highlighting in particular the conditions on the jump sets. Such conditions are expressed by means of traces of geometrically meaningful vector fields and characterized as pointwise limits of averages on cylinders with axes parallel to the unit normals to the jump sets.</p>","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90749172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning 基于自相似学习的单幅图像超分辨率非局部潜在低秩稀疏表示
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021017
Chang-Jin Song, Yun Wang
{"title":"Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning","authors":"Chang-Jin Song, Yun Wang","doi":"10.3934/IPI.2021017","DOIUrl":"https://doi.org/10.3934/IPI.2021017","url":null,"abstract":"In this paper, we propose a novel scheme for single image super resolution (SR) reconstruction. Firstly, we construct a new self-similarity framework by regarding the low resolution (LR) images as the low rank version of corresponding high resolution (HR) images. Subsequently, nuclear norm minimization (NNM) is employed to generate LR image pyramids from HR ones. The structure of our framework is beneficial to extract LR features, where we regard the quotient image, calculated between HR image and LR image at the same layer, as LR feature. This LR feature has the same dimension as LR image; however the dimension of commonly used gradient feature is 4 times than LR image. On the other hand, we employ nonlocal similar patch, within the same scale and across different scales, to generate HR and LR dictionaries. In the course of encoding, codes are calculated from both row and column of LR dictionary for each LR patch; at the same time, both low rank and sparse constraints on codes matrix give us a hand to remove coding noises. Finally, both quantitative and perceptual results demonstrate that our proposed method has a good SR performance.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90804218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography 二维电阻抗断层成像中系统伪影非线性傅立叶域的自动滤波
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021066
M. Alsaker, Benjamin Bladow, S. Campbell, Emma M. Kar
{"title":"Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography","authors":"M. Alsaker, Benjamin Bladow, S. Campbell, Emma M. Kar","doi":"10.3934/ipi.2021066","DOIUrl":"https://doi.org/10.3934/ipi.2021066","url":null,"abstract":"For patients undergoing mechanical ventilation due to respiratory failure, 2D electrical impedance tomography (EIT) is emerging as a means to provide functional monitoring of pulmonary processes. In EIT, electrical current is applied to the body, and the internal conductivity distribution is reconstructed based on subsequent voltage measurements. However, EIT images are known to often suffer from large systematic artifacts arising from various limitations and exacerbated by the ill-posedness of the inverse problem. The direct D-bar reconstruction method admits a nonlinear Fourier analysis of the EIT problem, providing the ability to process and filter reconstructions in the nonphysical frequency regime. In this work, a technique is introduced for automated Fourier-domain filtering of known systematic artifacts in 2D D-bar reconstructions. The new method is validated using three numerically simulated static thoracic datasets with induced artifacts, plus two experimental dynamic human ventilation datasets containing systematic artifacts. Application of the method is shown to significantly reduce the appearance of artifacts and improve the shape of the lung regions in all datasets.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89765697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates 用Carleman估计求解任意维半阶时间分数扩散方程的反问题
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2020-10-20 DOI: 10.3934/IPI.2021040
Xinchi Huang, A. Kawamoto
{"title":"Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates","authors":"Xinchi Huang, A. Kawamoto","doi":"10.3934/IPI.2021040","DOIUrl":"https://doi.org/10.3934/IPI.2021040","url":null,"abstract":"We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish the stability estimate of Lipschitz type in the inverse problems and the proofs are based on the Bukhgeim-Klibanov method by using Carleman estimates.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88552115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations 具有低阶非线性扰动的分数阶拉普拉斯方程的反问题
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2020-09-16 DOI: 10.3934/ipi.2021051
Ru-Yu Lai, Laurel Ohm
{"title":"Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations","authors":"Ru-Yu Lai, Laurel Ohm","doi":"10.3934/ipi.2021051","DOIUrl":"https://doi.org/10.3934/ipi.2021051","url":null,"abstract":"We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81428000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 14
Uniqueness and numerical reconstruction for inverse problems dealing with interval size search 区间大小搜索逆问题的唯一性与数值重构
IF 1.3 4区 数学
Inverse Problems and Imaging Pub Date : 2020-09-07 DOI: 10.3934/ipi.2021062
J. Apraiz, J. Cheng, A. Doubova, E. Fern'andez-Cara, M. Yamamoto
{"title":"Uniqueness and numerical reconstruction for inverse problems dealing with interval size search","authors":"J. Apraiz, J. Cheng, A. Doubova, E. Fern'andez-Cara, M. Yamamoto","doi":"10.3934/ipi.2021062","DOIUrl":"https://doi.org/10.3934/ipi.2021062","url":null,"abstract":"We consider a heat equation and a wave equation in one spatial dimension. This article deals with the inverse problem of determining the size of the spatial interval from some extra boundary information on the solution. Under several different circumstances, we prove uniqueness, non-uniqueness and some size estimates. Moreover, we numerically solve the inverse problems and compute accurate approximations of the size. This is illustrated with several satisfactory numerical experiments.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73280488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
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