Inverse Problems and Imaging最新文献_第6页

Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation 声学亥姆霍兹方程部分数据Calderón问题的Runge逼近与稳定性改进

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-11 DOI: 10.3934/ipi.2021049

M. Garc'ia-Ferrero, Angkana Ruland, Wiktoria Zato'n

引用次数: 5

Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods 利用高效水平集方法同时恢复反重力测量中的域和变密度

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2020073

Wenbin Li, J. Qian

{"title":"Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods","authors":"Wenbin Li, J. Qian","doi":"10.3934/ipi.2020073","DOIUrl":"https://doi.org/10.3934/ipi.2020073","url":null,"abstract":"We develop new efficient algorithms for a class of inverse problems of gravimetry to recover an anomalous volume mass distribution (measure) in the sense that we design fast local level-set methods to simultaneously reconstruct both unknown domain and varying density of the anomalous measure from modulus of gravity force rather than from gravity force itself. The equivalent-source principle of gravitational potential forces us to consider only measures of the form begin{document}$ mu = f,chi_{D} $end{document} , where begin{document}$ f $end{document} is a density function and begin{document}$ D $end{document} is a domain inside a closed set in begin{document}$ bf{R}^n $end{document} . Accordingly, various constraints are imposed upon both the density function and the domain so that well-posedness theories can be developed for the corresponding inverse problems, such as the domain inverse problem, the density inverse problem, and the domain-density inverse problem. Starting from uniqueness theorems for the domain-density inverse problem, we derive a new gradient from the misfit functional to enforce the directional-independence constraint of the density function and we further introduce a new labeling function into the level-set method to enforce the geometrical constraint of the corresponding domain; consequently, we are able to recover simultaneously both unknown domain and varying density from given modulus of gravity force. Our fast level-set method is built upon localizing the level-set evolution around a narrow band near the zero level-set and upon accelerating numerical modeling by novel low-rank matrix multiplication. Numerical results demonstrate that uniqueness theorems are crucial for solving the inverse problem of gravimetry and will be impactful on gravity prospecting. To the best of our knowledge, our inversion algorithm is the first of such for the domain-density inverse problem since it is based upon the conditional well-posedness theory of the inverse problem.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"37 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86831100","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

Two-dimensional inverse scattering for quasi-linear biharmonic operator 准线性双调和算子的二维逆散射

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021026

M. Harju, Jaakko Kultima, V. Serov, Teemu Tyni

引用次数: 3

A mathematical perspective on radar interferometry 雷达干涉测量的数学透视

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021043

M. Gilman, S. Tsynkov

{"title":"A mathematical perspective on radar interferometry","authors":"M. Gilman, S. Tsynkov","doi":"10.3934/ipi.2021043","DOIUrl":"https://doi.org/10.3934/ipi.2021043","url":null,"abstract":"Radar interferometry is an advanced remote sensing technology that utilizes complex phases of two or more radar images of the same target taken at slightly different imaging conditions and/or different times. Its goal is to derive additional information about the target, such as elevation. While this kind of task requires centimeter-level accuracy, the interaction of radar signals with the target, as well as the lack of precision in antenna position and other disturbances, generate ambiguities in the image phase that are orders of magnitude larger than the effect of interest.Yet the common exposition of radar interferometry in the literature often skips such topics. This may lead to unrealistic requirements for the accuracy of determining the parameters of imaging geometry, unachievable precision of image co-registration, etc. To address these deficiencies, in the current work we analyze the problem of interferometric height reconstruction and provide a careful and detailed account of all the assumptions and requirements to the imaging geometry and data processing needed for a successful extraction of height information from the radar data. We employ two most popular scattering models for radar targets: an isolated point scatterer and delta-correlated extended scatterer, and highlight the similarities and differences between them.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"55 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88401947","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

Edge detection with mixed noise based on maximum a posteriori approach 基于最大后验方法的混合噪声边缘检测

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021035

Yuying Shi, Zi-peng Liu, Xiaoying Wang, Jinping Zhang

引用次数: 1

A wavelet frame constrained total generalized variation model for imaging conductivity distribution 成像电导率分布的小波框架约束全广义变分模型

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021074

Yanyan Shi, Zhiwei Tian, Meng Wang, Xiaolong Kong, Lei Li, F. Fu

{"title":"A wavelet frame constrained total generalized variation model for imaging conductivity distribution","authors":"Yanyan Shi, Zhiwei Tian, Meng Wang, Xiaolong Kong, Lei Li, F. Fu","doi":"10.3934/ipi.2021074","DOIUrl":"https://doi.org/10.3934/ipi.2021074","url":null,"abstract":"Electrical impedance tomography (EIT) is a sensing technique with which conductivity distribution can be reconstructed. It should be mentioned that the reconstruction is a highly ill-posed inverse problem. Currently, the regularization method has been an effective approach to deal with this problem. Especially, total variation regularization method is advantageous over Tikhonov method as the edge information can be well preserved. Nevertheless, the reconstructed image shows severe staircase effect. In this work, to enhance the quality of reconstruction, a novel hybrid regularization model which combines a total generalized variation method with a wavelet frame approach (TGV-WF) is proposed. An efficient mean doubly augmented Lagrangian algorithm has been developed to solve the TGV-WF model. To demonstrate the effectiveness of the proposed method, numerical simulation and experimental validation are conducted for imaging conductivity distribution. Furthermore, some comparisons are made with typical regularization methods. From the results, it can be found that the proposed method shows better performance in the reconstruction since the edge of the inclusion can be well preserved and the staircase effect is effectively relieved.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"37 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87519380","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

Automatic extraction of cell nuclei using dilated convolutional network 基于扩张卷积网络的细胞核自动提取

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2020049

Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao, Yan Cao

{"title":"Automatic extraction of cell nuclei using dilated convolutional network","authors":"Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao, Yan Cao","doi":"10.3934/ipi.2020049","DOIUrl":"https://doi.org/10.3934/ipi.2020049","url":null,"abstract":"Pathological examination has been done manually by visual inspection of hematoxylin and eosin (H&E)-stained images. However, this process is labor intensive, prone to large variations, and lacking reproducibility in the diagnosis of a tumor. We aim to develop an automatic workflow to extract different cell nuclei found in cancerous tumors portrayed in digital renderings of the H&E-stained images. For a given image, we propose a semantic pixel-wise segmentation technique using dilated convolutions. The architecture of our dilated convolutional network (DCN) is based on SegNet, a deep convolutional encoder-decoder architecture. For the encoder, all the max pooling layers in the SegNet are removed and the convolutional layers are replaced by dilated convolution layers with increased dilation factors to preserve image resolution. For the decoder, all max unpooling layers are removed and the convolutional layers are replaced by dilated convolution layers with decreased dilation factors to remove gridding artifacts. We show that dilated convolutions are superior in extracting information from textured images. We test our DCN network on both synthetic data sets and a public available data set of H&E-stained images and achieve better results than the state of the art.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"4 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80442336","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

IPI special issue on 'mathematical/statistical approaches in data science' in the Inverse Problem and Imaging 关于“数据科学中的数学/统计方法”的IPI特刊在逆问题和成像中

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2021007

Weihong Guo, Y. Lou, Jing Qin, Ming Yan

{"title":"IPI special issue on 'mathematical/statistical approaches in data science' in the Inverse Problem and Imaging","authors":"Weihong Guo, Y. Lou, Jing Qin, Ming Yan","doi":"10.3934/ipi.2021007","DOIUrl":"https://doi.org/10.3934/ipi.2021007","url":null,"abstract":"Data science is an interdisciplinary field about extracting knowledge or insights from data. It involves computational and applied mathematics, statistics, computer science, engineering, and domain sciences. In an effort to bring together researchers from different disciplines to report on cutting-edge methodologies in data science, Dr. Yifei Lou at the University of Texas at Dallas (UTD), together with Drs. Weihong Guo (Case Western Reserve University), Jing Qin (University of Kentucky), and Ming Yan (Michigan State University), organized a workshop, entitled “Recent Developments on Mathematical/Statistical Approaches in Data Science,” held at the UTD’s campus, on June 1-June 2 2019. To better disseminate the results, this special issue in the journal of Inverse Problems and Imaging (IPI) assembles peer reviewed articles from some of the invited speakers. The scope of the special issue is centered at data science, aiming to collect state-of-the-art computational algorithms and novel applications in data processing. The topics range from compressive sensing, machine learning, image processing, variational and PDE-based models, large-scale optimization, and data-driven applications.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"21 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73000965","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

The interior transmission eigenvalue problem for elastic waves in media with obstacles 有障碍物介质中弹性波的内部传播特征值问题

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/ipi.2020075

F. Cakoni, Pu-Zhao Kow, Jenn-Nan Wang

引用次数: 5

Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications 求解复合单调包含问题的预条件Douglas-Rachford型原对偶方法及其应用

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI: 10.3934/IPI.2021014

Yixuan Yang, Yuchao Tang, Meng Wen, T. Zeng

引用次数: 5