Inverse Problems最新文献_第5页

Inverse problem of recovering a time-dependent nonlinearity appearing in third-order nonlinear acoustic equations * 恢复三阶非线性声学方程中出现的随时间变化的非线性的逆问题 *

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-05-23 DOI: 10.1088/1361-6420/ad49cd

Song-Ren Fu, Peng-Fei Yao and Yongyi Yu

引用次数: 0

Stability and statistical inversion of travel time tomography 旅行时间断层摄影的稳定性和统计反演

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-05-23 DOI: 10.1088/1361-6420/ad4911

Ashwin Tarikere and Hanming Zhou

引用次数: 0

Learning a stable approximation of an existing but unknown inverse mapping: Application to the half-time circular Radon transform 学习现有但未知反映射的稳定近似：半时循环拉顿变换的应用

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-05-22 DOI: 10.1088/1361-6420/ad4f0a

Refik Mert Çam, Umberto Villa, Mark A. Anastasio

{"title":"Learning a stable approximation of an existing but unknown inverse mapping: Application to the half-time circular Radon transform","authors":"Refik Mert Çam, Umberto Villa, Mark A. Anastasio","doi":"10.1088/1361-6420/ad4f0a","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4f0a","url":null,"abstract":"\u0000 Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as ``half-time\" measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141110224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Solving inverse obstacle scattering problem with latent surface representations 用潜在表面表示法解决反障碍物散射问题

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-05-15 DOI: 10.1088/1361-6420/ad466a

Junqing Chen, Bangti Jin and Haibo Liu

引用次数: 0

Local near-field scattering data enables unique reconstruction of rough electric potentials 局部近场散射数据实现了粗糙电势的独特重构

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-25 DOI: 10.1088/1361-6420/ad3eaa

Manuel Cañizares

引用次数: 0

Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation 时谐双谐波方程反腔散射问题的唯一性

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-25 DOI: 10.1088/1361-6420/ad438c

Heping Dong, Peijun Li

引用次数: 0

Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations 从阻尼波方程无限时间圆柱体上的解的轨迹重构初始数据

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-24 DOI: 10.1088/1361-6420/ad42cd

Seongyeon Kim, Sunghwan Moon, Ihyeok Seo

引用次数: 0

A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution 用于多光子显微镜图像复原的新型变分法：从 PSF 估计到 3D 解卷积

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-23 DOI: 10.1088/1361-6420/ad3c67

Julien Ajdenbaum, Emilie Chouzenoux, Claire Lefort, Ségolène Martin and Jean-Christophe Pesquet

{"title":"A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution","authors":"Julien Ajdenbaum, Emilie Chouzenoux, Claire Lefort, Ségolène Martin and Jean-Christophe Pesquet","doi":"10.1088/1361-6420/ad3c67","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3c67","url":null,"abstract":"In multi-photon microscopy (MPM), a recent in-vivo fluorescence microscopy system, the task of image restoration can be decomposed into two interlinked inverse problems: firstly, the characterization of the point spread function (PSF) and subsequently, the deconvolution (i.e. deblurring) to remove the PSF effect, and reduce noise. The acquired MPM image quality is critically affected by PSF blurring and intense noise. The PSF in MPM is highly spread in 3D and is not well characterized, presenting high variability with respect to the observed objects. This makes the restoration of MPM images challenging. Common PSF estimation methods in fluorescence microscopy, including MPM, involve capturing images of sub-resolution beads, followed by quantifying the resulting ellipsoidal 3D spot. In this work, we revisit this approach, coping with its inherent limitations in terms of accuracy and practicality. We estimate the PSF from the observation of relatively large beads (approximately 1 in diameter). This goes through the formulation and resolution of an original non-convex minimization problem, for which we propose a proximal alternating method along with convergence guarantees. Following the PSF estimation step, we then introduce an innovative strategy to deal with the high level multiplicative noise degrading the acquisitions. We rely on a heteroscedastic noise model for which we estimate the parameters. We then solve a constrained optimization problem to restore the image, accounting for the estimated PSF and noise, while allowing a minimal hyper-parameter tuning. Theoretical guarantees are given for the restoration algorithm. These algorithmic contributions lead to an end-to-end pipeline for 3D image restoration in MPM, that we share as a publicly available Python software. We demonstrate its effectiveness through several experiments on both simulated and real data.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 residual fully convolutional network (Res-FCN) for electromagnetic inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band 用于宽频带内任意频率高对比度散射体电磁反演的残差全卷积网络 (Res-FCN)

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-22 DOI: 10.1088/1361-6420/ad4171

Hao-Jie Hu, Jiawen Li, Li-Ye Xiao, Yu Cheng, Qing Huo Liu

{"title":"A residual fully convolutional network (Res-FCN) for electromagnetic inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band","authors":"Hao-Jie Hu, Jiawen Li, Li-Ye Xiao, Yu Cheng, Qing Huo Liu","doi":"10.1088/1361-6420/ad4171","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4171","url":null,"abstract":"\u0000 Many successful machine learning methods have been developed for electromagnetic inverse scattering problems. However, so far, their inversion has been performed only at the specifically trained frequencies. To make the machine learning based inversion method more generalizable for realistic engineering applications, this work proposes a residual fully convolutional network (Res-FCN) to perform EM inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band. The proposed Res-FCN combines the advantages of the Res-Net and the fully convolutional network (FCN). Res-FCN consists of an encoder and a decoder: the encoder is employed to extract high-dimensional features from the measured scattered field through the residual frameworks, while the decoder is employed to map from the high-dimensional features extracted by the encoder to the electrical parameter distribution in the inversion region by the up-sample layer and the residual frameworks. Four numerical examples verify that the proposed Res-FCN can achieve good performance in the 2-D EM inversion problem for high contrast scatterers with anti-noise ability at an arbitrary frequency point within a wide frequency band.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization 通过基于补丁的张量对数 Schatten-p 最小化实现三维泊松图像去模糊

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-19 DOI: 10.1088/1361-6420/ad40c9

Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou

引用次数: 0