SIAM Journal on Imaging Sciences最新文献_第5页

Analysis of View Aliasing for the Generalized Radon Transform in [math] 数学]中广义拉顿变换的视差分析

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-23 DOI: 10.1137/23m1554746

Alexander Katsevich

引用次数: 0

Learnable Nonlocal Self-Similarity of Deep Features for Image Denoising 用于图像去噪的深度特征的可学习非局部自相似性

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-23 DOI: 10.1137/22m1536996

Junying Meng, Faqiang Wang, Jun Liu

{"title":"Learnable Nonlocal Self-Similarity of Deep Features for Image Denoising","authors":"Junying Meng, Faqiang Wang, Jun Liu","doi":"10.1137/22m1536996","DOIUrl":"https://doi.org/10.1137/22m1536996","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 441-475, March 2024. Abstract. High-dimensional deep features extracted by convolutional neural networks have nonlocal self-similarity. However, incorporating this nonlocal prior of deep features into deep network architectures with an interpretable variational framework is rarely explored. In this paper, we propose a learnable nonlocal self-similarity deep feature network for image denoising. Our method is motivated by the fact that the high-dimensional deep features obey a mixture probability distribution based on the Parzen–Rosenblatt window method. Then a regularizer with learnable nonlocal weights is proposed by considering the dual representation of the log-probability prior of the deep features. Specifically, the nonlocal weights are introduced as dual variables that can be learned by unrolling the associated numerical scheme. This leads to nonlocal modules (NLMs) in newly designed networks. Our method provides a statistical and variational interpretation for the nonlocal self-attention mechanism widely used in various networks. By adopting nonoverlapping window and region decomposition techniques, we can significantly reduce the computational complexity of nonlocal self-similarity, thus enabling parallel computation of the NLM. The solution to the proposed variational problem can be formulated as a learnable nonlocal self-similarity network for image denoising. This work offers a novel approach for constructing network structures that consider self-similarity and nonlocality. The improvements achieved by this method are predictable and partially controllable. Compared with several closely related denoising methods, the experimental results show the effectiveness of the proposed method in image denoising.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"34 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Cortical V1 Transform as a Heterogeneous Poisson Problem 作为异质泊松问题的皮层 V1 变换

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-21 DOI: 10.1137/23m1555958

Alessandro Sarti, Mattia Galeotti, Giovanna Citti

引用次数: 0

The [math]-Laplace “Signature” for Quasilinear Inverse Problems 准线性反问题的[math]-拉普拉斯 "签名

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-15 DOI: 10.1137/22m1527192

Antonio Corbo Esposito, Luisa Faella, Gianpaolo Piscitelli, Vincenzo Mottola, Ravi Prakash, Antonello Tamburrino

{"title":"The [math]-Laplace “Signature” for Quasilinear Inverse Problems","authors":"Antonio Corbo Esposito, Luisa Faella, Gianpaolo Piscitelli, Vincenzo Mottola, Ravi Prakash, Antonello Tamburrino","doi":"10.1137/22m1527192","DOIUrl":"https://doi.org/10.1137/22m1527192","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 351-388, March 2024. Abstract. This paper refers to an imaging problem in the presence of nonlinear materials. Specifically, the problem we address falls within the framework of Electrical Resistance Tomography and involves two different materials, one or both of which are nonlinear. Tomography with nonlinear materials is in the early stages of development, although breakthroughs are expected in the not-too-distant future. The original contribution this work makes is that the nonlinear problem can be approximated by a weighted [math]-Laplace problem. From the perspective of tomography, this is a significant result because it highlights the central role played by the [math]-Laplacian in inverse problems with nonlinear materials. Moreover, when [math], this result allows all the imaging methods and algorithms developed for linear materials to be brought into the arena of problems with nonlinear materials. The main result of this work is that for “small” Dirichlet data, (i) one material can be replaced by a perfect electric conductor and (ii) the other material can be replaced by a material giving rise to a weighted [math]-Laplace problem.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"11 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment 多散射环境下单稳态数据的降阶建模反演

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-08 DOI: 10.1137/23m1564365

Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky

{"title":"Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment","authors":"Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky","doi":"10.1137/23m1564365","DOIUrl":"https://doi.org/10.1137/23m1564365","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 334-350, March 2024. Abstract.Data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of inverse scattering problems with applications to seismic and sonar imaging. One requirement of this approach is that it uses the full square multiple-input/multiple-output (MIMO) matrix-valued transfer function as the data for multidimensional problems. The synthetic aperture radar (SAR), however, is limited to the single-input/single-output (SISO) measurements corresponding to the diagonal of the matrix transfer function. Here we present a ROM-based Lippmann–Schwinger approach overcoming this drawback. The ROMs are constructed to match the data for each source-receiver pair separately, and these are used to construct internal solutions for the corresponding source using only the data-driven Gramian. Efficiency of the proposed approach is demonstrated on 2D and 2.5D (3D propagation and 2D reflectors) numerical examples. The new algorithm not only suppresses multiple echoes seen in the Born imaging but also takes advantage of their illumination of some back sides of the reflectors, improving the quality of their mapping.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"170 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Posterior-Variance–Based Error Quantification for Inverse Problems in Imaging 基于后验方差的成像逆问题误差量化

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-07 DOI: 10.1137/23m1546129

Dominik Narnhofer, Andreas Habring, Martin Holler, Thomas Pock

{"title":"Posterior-Variance–Based Error Quantification for Inverse Problems in Imaging","authors":"Dominik Narnhofer, Andreas Habring, Martin Holler, Thomas Pock","doi":"10.1137/23m1546129","DOIUrl":"https://doi.org/10.1137/23m1546129","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 301-333, March 2024. Abstract.In this work, a method for obtaining pixelwise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that, in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, a novel primal-dual Langevin algorithm for sampling from nonsmooth distributions is also introduced in this work, showing promising results in practice. While a proof of convergence for this primal-dual algorithm is still open, the theoretical guarantees of the proposed method do not require a guaranteed convergence of the sampling algorithm.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"170 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Majorization-Minimization Algorithm for Neuroimage Registration 神经图像注册的主要化-最小化算法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-05 DOI: 10.1137/22m1516907

Gaiting Zhou, Daniel Tward, Kenneth Lange

{"title":"A Majorization-Minimization Algorithm for Neuroimage Registration","authors":"Gaiting Zhou, Daniel Tward, Kenneth Lange","doi":"10.1137/22m1516907","DOIUrl":"https://doi.org/10.1137/22m1516907","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 273-300, March 2024. Abstract. Intensity-based image registration is critical for neuroimaging tasks, such as 3D reconstruction, times-series alignment, and common coordinate mapping. The gradient-based optimization methods commonly used to solve this problem require a careful selection of step-length. This limitation imposes substantial time and computational costs. Here we propose a gradient-independent rigid-motion registration algorithm based on the majorization-minimization (MM) principle. Each iteration of our intensity-based MM algorithm reduces to a simple point-set rigid registration problem with a closed form solution that avoids the step-length issue altogether. The details of the algorithm are presented, and an error bound for its more practical truncated form is derived. The performance of the MM algorithm is shown to be more effective than gradient descent on simulated images and Nissl stained coronal slices of mouse brain. We also compare and contrast the similarities and differences between the MM algorithm and another gradient-free registration algorithm called the block-matching method. Finally, extensions of this algorithm to more complex problems are discussed.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"23 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Image Segmentation Using Bayesian Inference for Convex Variant Mumford–Shah Variational Model 利用贝叶斯推理进行凸变孟福德-沙赫变分模型的图像分割

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-01-30 DOI: 10.1137/23m1545379

Xu Xiao, Youwei Wen, Raymond Chan, Tieyong Zeng

{"title":"Image Segmentation Using Bayesian Inference for Convex Variant Mumford–Shah Variational Model","authors":"Xu Xiao, Youwei Wen, Raymond Chan, Tieyong Zeng","doi":"10.1137/23m1545379","DOIUrl":"https://doi.org/10.1137/23m1545379","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 248-272, March 2024. Abstract. The Mumford–Shah model is a classical segmentation model, but its objective function is nonconvex. The smoothing and thresholding (SaT) approach is a convex variant of the Mumford–Shah model, which seeks a smoothed approximation solution to the Mumford–Shah model. The SaT approach separates the segmentation into two stages: first, a convex energy function is minimized to obtain a smoothed image; then, a thresholding technique is applied to segment the smoothed image. The energy function consists of three weighted terms and the weights are called the regularization parameters. Selecting appropriate regularization parameters is crucial to achieving effective segmentation results. Traditionally, the regularization parameters are chosen by trial-and-error, which is a very time-consuming procedure and is not practical in real applications. In this paper, we apply a Bayesian inference approach to infer the regularization parameters and estimate the smoothed image. We analyze the convex variant Mumford–Shah variational model from a statistical perspective and then construct a hierarchical Bayesian model. A mean field variational family is used to approximate the posterior distribution. The variational density of the smoothed image is assumed to have a Gaussian density, and the hyperparameters are assumed to have Gamma variational densities. All the parameters in the Gaussian density and Gamma densities are iteratively updated. Experimental results show that the proposed approach is capable of generating high-quality segmentation results. Although the proposed approach contains an inference step to estimate the regularization parameters, it requires less CPU running time to obtain the smoothed image than previous methods.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"217 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptions 稳健的张量 CUR 分解：利用稀疏破坏快速恢复低塔克等级张量

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-01-25 DOI: 10.1137/23m1574282

HanQin Cai, Zehan Chao, Longxiu Huang, Deanna Needell

引用次数: 0

Direct Imaging Methods for Reconstructing a Locally Rough Interface from Phaseless Total-Field Data or Phased Far-Field Data 根据无相全场数据或相位远场数据重建局部粗糙界面的直接成像方法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-01-24 DOI: 10.1137/23m1571393

Long Li, Jiansheng Yang, Bo Zhang, Haiwen Zhang

{"title":"Direct Imaging Methods for Reconstructing a Locally Rough Interface from Phaseless Total-Field Data or Phased Far-Field Data","authors":"Long Li, Jiansheng Yang, Bo Zhang, Haiwen Zhang","doi":"10.1137/23m1571393","DOIUrl":"https://doi.org/10.1137/23m1571393","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 188-224, March 2024. Abstract. This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in two dimensions. A direct imaging method is proposed to reconstruct the locally rough interface from the phaseless total-field data measured on the upper half of the circle with a large radius at a fixed frequency or from the phased far-field data measured on the upper half of the unit circle at a fixed frequency. The presence of the locally rough interface poses challenges in the theoretical analysis of the imaging methods. To address these challenges, a technically involved asymptotic analysis is provided for the relevant oscillatory integrals involved in the imaging methods, based mainly on the techniques and results in our recent work [L. Li, J. Yang, B. Zhang, and H. Zhang, arXiv:2208.00456, 2022] on the uniform far-field asymptotics of the scattered field for acoustic scattering in a two-layered medium. Finally, extensive numerical experiments are conducted to demonstrate the feasibility and robustness of our imaging algorithms.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"255 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139555072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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