Inverse Problems and Imaging最新文献_第2页

Imaging of conductivity distribution based on a combined reconstruction method in brain electrical impedance tomography 脑电阻抗断层成像中电导率分布的联合重建方法

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2022060

Yanyan Shi, Yajun Lou, Meng Wang, Shuo Zheng, Zhiwei Tian, Feng Fu

{"title":"Imaging of conductivity distribution based on a combined reconstruction method in brain electrical impedance tomography","authors":"Yanyan Shi, Yajun Lou, Meng Wang, Shuo Zheng, Zhiwei Tian, Feng Fu","doi":"10.3934/ipi.2022060","DOIUrl":"https://doi.org/10.3934/ipi.2022060","url":null,"abstract":"Electrical impedance tomography (EIT) is a promising technique in medical imaging. With this technique, pathology-related conductivity variation can be visualized. Nevertheless, reconstruction of conductivity distribution is a severely ill-posed inverse problem which poses a great challenge for the EIT technique. Especially in brain EIT, irregular and multi-layered head structure along with low-conductivity skull brings more difficulties for accurate reconstruction. To address such problems, a novel reconstruction method which combines Tikhonov regularization with denoising algorithm is proposed for imaging conductivity distribution in brain EIT. With the proposed method, image reconstruction of intracerebral hemorrhage in different brain lobes of a three-layer head model is conducted. Besides, simultaneous reconstruction of intracerebral hemorrhage and secondary ischemia is performed. Meanwhile, the impact of noise is investigated to evaluate the anti-noise performance. In addition, image reconstructions under head shape deformation are performed. The proposed reconstruction method is also quantitatively estimated by calculating blur radius and structural similarity. Phantom experiments are carried out to further verify the effectiveness of the proposed method. Both qualitative and quantitative results have demonstrated that the proposed combined method is superior to Tikhonov regularization in imaging conductivity distribution. This work would provide an alternative for accurate reconstruction in EIT based medical imaging.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134955520","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

Self-supervised multi-scale neural network for blind deblurring 用于盲去模糊的自监督多尺度神经网络

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2023046

Meina Zhang, Ying Yang, Guoxi Ni, Tingting Wu, Tieyong Zeng

{"title":"Self-supervised multi-scale neural network for blind deblurring","authors":"Meina Zhang, Ying Yang, Guoxi Ni, Tingting Wu, Tieyong Zeng","doi":"10.3934/ipi.2023046","DOIUrl":"https://doi.org/10.3934/ipi.2023046","url":null,"abstract":"Blurry kernel estimation is a critical yet challenging task for blind deblurring. Most existing works devote to designing end-to-end networks that require a large amount of hard-to-obtain training data. In addition, these methods often ignore the intrinsic effects of blur kernel for blind deblurring. In this work, we present a unified latent image deblur and kernel estimation method based on MAP framework. By revisiting the coarse-to-fine strategy, we introduce a self-supervised multi-scale deblur network(MD-Net), where the multi-scale structure significantly reduce the kernel deviation caused by local area minimization. Specifically, our network commences with random inputs and outputs multi-scale reconstructed images and kernels. By progressively capturing the high-level configuration and low-level details from matching multi-resolution loss functions, the proposed MD-Net enable to capture multi-level image priors. Meanwhile, at each coarse level, we use Feature Extraction(FE) layers to further extract and emphasize features from reconstructed images. Compared with state-of-the-art blind deblurring methods, extensive experiments demonstrate that the proposed approach significantly improves the restoration performance in both quantitative and qualitative evaluations.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135560496","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

A Wasserstein distance and total variation regularized model for image reconstruction problems 图像重建问题的Wasserstein距离和总变分正则化模型

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2023045

Yiming Gao

引用次数: 0

Super-resolution surface reconstruction from few low-resolution slices 基于少量低分辨率切片的超分辨率表面重建

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2023040

Yiyao Zhang, Ke Chen, Shang-Hua Yang

引用次数: 0

Stability for the inverse source problem in a two-layered medium separated by rough interface 由粗糙界面分离的两层介质中逆源问题的稳定性

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2023047

Guanghui Hu, Xiang Xu, Xiaokai Yuan, Yue Zhao

引用次数: 0

Corrigendum to "duality between range and no-response tests and its application for inverse problems" "极差和无响应检验的对偶性及其在反问题中的应用"的勘误表

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2023003

Yi-Hsuan Lin, Gen Nakamura, Roland Potthast, Haibing Wang

引用次数: 1

Determination of piecewise homogeneous sources for elastic and electromagnetic waves 弹性波和电磁波分段均匀源的测定

4区数学

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI: 10.3934/ipi.2022065

Jian Zhai, Yue Zhao

引用次数: 1

Recovery of a potential on a quantum star graph from Weyl's matrix 从Weyl矩阵中恢复量子星图上的势

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2022-10-27 DOI: 10.3934/ipi.2023034

S. Avdonin, K. V. Khmelnytskaya, V. Kravchenko

{"title":"Recovery of a potential on a quantum star graph from Weyl's matrix","authors":"S. Avdonin, K. V. Khmelnytskaya, V. Kravchenko","doi":"10.3934/ipi.2023034","DOIUrl":"https://doi.org/10.3934/ipi.2023034","url":null,"abstract":"The problem of recovery of a potential on a quantum star graph from Weyl's matrix given at a finite number of points is considered. A method for its approximate solution is proposed. It consists in reducing the problem to a two-spectra inverse Sturm-Liouville problem on each edge with its posterior solution. The overall approach is based on Neumann series of Bessel functions (NSBF) representations for solutions of Sturm-Liouville equations, and, in fact, the solution of the inverse problem on the quantum graph reduces to dealing with the NSBF coefficients. The NSBF representations admit estimates for the series remainders which are independent of the real part of the square root of the spectral parameter. This feature makes them especially useful for solving direct and inverse problems requiring calculation of solutions on large intervals in the spectral parameter. Moreover, the first coefficient of the NSBF representation alone is sufficient for the recovery of the potential. The knowledge of the Weyl matrix at a set of points allows one to calculate a number of the NSBF coefficients at the end point of each edge, which leads to approximation of characteristic functions of two Sturm-Liouville problems and allows one to compute the Dirichlet-Dirichlet and Neumann-Dirichlet spectra on each edge. In turn, for solving this two-spectra inverse Sturm-Liouville problem a system of linear algebraic equations is derived for computing the first NSBF coefficient and hence for recovering the potential. The proposed method leads to an efficient numerical algorithm that is illustrated by a number of numerical tests.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42934184","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

On the range of the $ X $-ray transform of symmetric tensors compactly supported in the plane 在平面上紧支撑的对称张量的X射线变换的范围

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2022-09-19 DOI: 10.3934/ipi.2022070

K. Sadiq, A. Tamasan

引用次数: 3

On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients 含时相关系数的非耦合时空分数算子的反问题

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2022-08-09 DOI: 10.3934/ipi.2023008

Li Li

引用次数: 4