Inverse Problems and Imaging最新文献_第10页

Interactions of semilinear progressing waves in two or more space dimensions 二维或多维空间中半线性行进波的相互作用

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-29 DOI: 10.3934/ipi.2020055

Antonio S'a Barreto

引用次数: 13

RWRM: Residual Wasserstein regularization model for image restoration RWRM:残差Wasserstein正则化模型用于图像恢复

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2020069

Ruiqiang He, Xiangchu Feng, Xiaolong Zhu, Hua Huang, Bingzhe Wei

引用次数: 1

Integral formulation of the complete electrode model of electrical impedance tomography 电阻抗层析成像全电极模型的积分公式

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2020017

Erfang Ma

引用次数: 4

$ chi^2 $ test for total variation regularization parameter selection $ chi^2 $检验用于总变分正则化参数选择

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2020019

J. Mead

{"title":"$ chi^2 $ test for total variation regularization parameter selection","authors":"J. Mead","doi":"10.3934/ipi.2020019","DOIUrl":"https://doi.org/10.3934/ipi.2020019","url":null,"abstract":"Total Variation (TV) is an effective method of removing noise in digital image processing while preserving edges. The scaling or regularization parameter in the TV process defines the amount of denoising, with a value of zero giving a result equivalent to the input signal. The discrepancy principle is a classical method for regularization parameter selection whereby data is fit to a specified tolerance. The tolerance is often identified based on the fact that the least squares data fit is known to follow a begin{document}$ chi^2 $end{document} distribution. However, this approach fails when the number of parameters is greater than or equal to the number of data. Typically, heuristics are employed to identify the tolerance in the discrepancy principle and this leads to oversmoothing. In this work we identify a begin{document}$ chi^2 $end{document} test for TV regularization parameter selection assuming the blurring matrix is full rank. In particular, we prove that the degrees of freedom in the TV regularized residual is the number of data and this is used to identify the appropriate tolerance. The importance of this work lies in the fact that the begin{document}$ chi^2 $end{document} test introduced here for TV automates the choice of regularization parameter selection and can straightforwardly be incorporated into any TV algorithm. Results are given for three test images and compared to results using the discrepancy principle and MAP estimates.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74654057","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: 5

Nonlocal TV-Gaussian prior for Bayesian inverse problems with applications to limited CT reconstruction 贝叶斯反问题的非局部tv -高斯先验及其在有限CT重建中的应用

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2019066

Didi Lv, Qingping Zhou, Jae Kyu Choi, Jinglai Li, Xiaoqun Zhang

{"title":"Nonlocal TV-Gaussian prior for Bayesian inverse problems with applications to limited CT reconstruction","authors":"Didi Lv, Qingping Zhou, Jae Kyu Choi, Jinglai Li, Xiaoqun Zhang","doi":"10.3934/ipi.2019066","DOIUrl":"https://doi.org/10.3934/ipi.2019066","url":null,"abstract":"Bayesian inference methods have been widely applied in inverse problems due to the ability of uncertainty characterization of the estimation. The prior distribution of the unknown plays an essential role in the Bayesian inference, and a good prior distribution can significantly improve the inference results. In this paper, we propose a hybrid prior distribution on combining the nonlocal total variation regularization (NLTV) and the Gaussian distribution, namely NLTG prior. The advantage of this hybrid prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the hybrid prior. We apply the proposed prior to limited tomography reconstruction problem that is difficult due to severe data missing. Both maximum a posteriori and conditional mean estimates are computed through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":"133 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89125379","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: 9

Unique determinations in inverse scattering problems with phaseless near-field measurements 无相近场测量反散射问题的独特确定

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2020026

Deyue Zhang, Yukun Guo, Fenglin Sun, Hongyu Liu

引用次数: 14

Extended sampling method for interior inverse scattering problems 内部逆散射问题的扩展采样方法

IF 1.3 4区数学

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI: 10.3934/ipi.2020033

Fang Zeng

引用次数: 0

An adaptive total variational despeckling model based on gray level indicator frame 基于灰度指标框架的自适应全变分去斑模型