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

Numerical Implementation of Generalized V-Line Transforms on 2D Vector Fields and their Inversions 二维矢量场的广义 V 型线变换及其反演的数值实现

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-03-07 DOI: 10.1137/23m1573112

Gaik Ambartsoumian, Mohammad J. Latifi Jebelli, Rohit K. Mishra

引用次数: 0

A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry Applied to Imaging 将准共形几何应用于成像的深度学习框架，用于解决衍射映射问题

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-03-05 DOI: 10.1137/22m1516099

Qiguang Chen, Zhiwen Li, Lok Ming Lui

{"title":"A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry Applied to Imaging","authors":"Qiguang Chen, Zhiwen Li, Lok Ming Lui","doi":"10.1137/22m1516099","DOIUrl":"https://doi.org/10.1137/22m1516099","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 501-539, March 2024. Abstract. Many imaging problems can be formulated as mapping problems. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems are often inefficient and can sometimes get trapped in local minima. An extra challenge arises when the optimal mapping is required to be diffeomorphic. In this work, we address the problem by proposing a deep-learning framework based on the Quasiconformal (QC) Teichmüller theories. The main strategy is to learn the Beltrami coefficient (BC) that represents a mapping as the latent feature vector in the deep neural network. The BC measures the local geometric distortion under the mapping, with which the interpretability of the deep neural network can be enhanced. Under this framework, the diffeomorphic property of the mapping can be controlled via a simple activation function within the network. The optimal mapping can also be easily regularized by integrating the BC into the loss function. A crucial advantage of the proposed framework is that once the network is successfully trained, the optimized mapping corresponding to each input data information can be obtained in real time. To examine the efficacy of the proposed framework, we apply the method to the diffeomorphic image registration problem. Experimental results outperform other state-of-the-art registration algorithms in both efficiency and accuracy, which demonstrate the effectiveness of our proposed framework to solve the mapping problem.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036956","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

Fractional Fourier Transforms Meet Riesz Potentials and Image Processing 分数傅里叶变换与里兹势和图像处理的结合

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-02-27 DOI: 10.1137/23m1555442

Zunwei Fu, Yan Lin, Dachun Yang, Shuhui Yang

引用次数: 0

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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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