SIAM Journal on Imaging Sciences最新文献_第2页

Proximal Langevin Sampling with Inexact Proximal Mapping 近端朗格文采样与非精确近端映射

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-30 DOI: 10.1137/23m1593565

Matthias J. Ehrhardt, Lorenz Kuger, Carola-Bibiane Schönlieb

{"title":"Proximal Langevin Sampling with Inexact Proximal Mapping","authors":"Matthias J. Ehrhardt, Lorenz Kuger, Carola-Bibiane Schönlieb","doi":"10.1137/23m1593565","DOIUrl":"https://doi.org/10.1137/23m1593565","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1729-1760, September 2024. Abstract. In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional posteriors, Markov chain Monte Carlo methods based on time discretizations of Langevin diffusion are a popular tool. If the potential defining the distribution is nonsmooth, these discretizations are usually of an implicit form leading to Langevin sampling algorithms that require the evaluation of proximal operators. For some of the potentials relevant in imaging problems this is only possible approximately using an iterative scheme. We investigate the behavior of a proximal Langevin algorithm under the presence of errors in the evaluation of proximal mappings. We generalize existing nonasymptotic and asymptotic convergence results of the exact algorithm to our inexact setting and quantify the bias between the target and the algorithm’s stationary distribution due to the errors. We show that the additional bias stays bounded for bounded errors and converges to zero for decaying errors in a strongly convex setting. We apply the inexact algorithm to sample numerically from the posterior of typical imaging inverse problems in which we can only approximate the proximal operator by an iterative scheme and validate our theoretical convergence results.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"192 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864204","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

Three-Stage Approach for 2D/3D Diffeomorphic Multimodality Image Registration with Textural Control 利用纹理控制实现二维/三维差分多模态图像配准的三阶段方法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-26 DOI: 10.1137/23m1583971

Ke Chen, Huan Han

引用次数: 0

Discrete Morphological Neural Networks 离散形态神经网络

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-25 DOI: 10.1137/23m1598477

Diego Marcondes, Junior Barrera

{"title":"Discrete Morphological Neural Networks","authors":"Diego Marcondes, Junior Barrera","doi":"10.1137/23m1598477","DOIUrl":"https://doi.org/10.1137/23m1598477","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1650-1689, September 2024. Abstract.A classical approach to designing binary image operators is mathematical morphology (MM). We propose the Discrete Morphological Neural Networks (DMNN) for binary image analysis to represent W-operators and estimate them via machine learning. A DMNN architecture, which is represented by a morphological computational graph, is designed as in the classical heuristic design of morphological operators, in which the designer should combine a set of MM operators and Boolean operations based on prior information and theoretical knowledge. Then, once the architecture is fixed, instead of adjusting its parameters (i.e., structuring elements or maximal intervals) by hand, we propose a lattice descent algorithm (LDA) to train these parameters based on a sample of input and output images under the usual machine learning approach. We also propose a stochastic version of the LDA that is more efficient, is scalable, and can obtain small error in practical problems. The class represented by a DMNN can be quite general or specialized according to expected properties of the target operator, i.e., prior information, and the semantic expressed by algebraic properties of classes of operators is a differential relative to other methods. The main contribution of this paper is the merger of the two main paradigms for designing morphological operators: classical heuristic design and automatic design via machine learning. As a proof-of-concept, we apply the DMNN to recognize the boundary of digits with noise, and we discuss many topics for future research.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"33 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141773778","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

Localization of Point Scatterers via Sparse Optimization on Measures 通过测量稀疏优化实现点散射体定位

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-23 DOI: 10.1137/24m1636265

Giovanni S. Alberti, Romain Petit, Matteo Santacesaria

引用次数: 0

Tight-Frame-Like Analysis-Sparse Recovery Using Nontight Sensing Matrices 紧框架分析--使用非紧传感矩阵进行解析恢复

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-17 DOI: 10.1137/23m1625846

Kartheek Kumar Reddy Nareddy, Abijith Jagannath Kamath, Chandra Sekhar Seelamantula

{"title":"Tight-Frame-Like Analysis-Sparse Recovery Using Nontight Sensing Matrices","authors":"Kartheek Kumar Reddy Nareddy, Abijith Jagannath Kamath, Chandra Sekhar Seelamantula","doi":"10.1137/23m1625846","DOIUrl":"https://doi.org/10.1137/23m1625846","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1587-1618, September 2024. Abstract.The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques. However, tight-frame sensing matrices result in minimum mean-squared-error recovery given oracle knowledge of the support of the sparse vector. If the sensing matrix is not tight, could one achieve the recovery performance assured by a tight frame by suitably designing the recovery strategy? This is the key question addressed in this paper. We consider the analysis-sparse [math]-minimization problem with a generalized [math]-norm-based data-fidelity and show that it effectively corresponds to using a tight-frame sensing matrix. The new formulation offers improved performance bounds when the number of nonzeros is large. One could develop a tight-frame variant of a known sparse recovery algorithm using the proposed formalism. We solve the analysis-sparse recovery problem in an unconstrained setting using proximal methods. Within the tight-frame sensing framework, we rescale the gradients of the data-fidelity loss in the iterative updates to further improve the accuracy of analysis-sparse recovery. Experimental results show that the proposed algorithms offer superior analysis-sparse recovery performance. Proceeding further, we also develop deep-unfolded variants, with a convolutional neural network as the sparsifying operator. On the application front, we consider compressed sensing image recovery. Experimental results on Set11, BSD68, Urban100, and DIV2K datasets show that the proposed techniques outperform the state-of-the-art techniques, with performance measured in terms of peak signal-to-noise ratio and structural similarity index metric.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"40 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722573","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

Imaging of Atmospheric Dispersion Processes with Differential Absorption Lidar 利用差分吸收激光雷达成像大气弥散过程

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-12 DOI: 10.1137/23m1598404

Robert Lung, Nick Polydorides

{"title":"Imaging of Atmospheric Dispersion Processes with Differential Absorption Lidar","authors":"Robert Lung, Nick Polydorides","doi":"10.1137/23m1598404","DOIUrl":"https://doi.org/10.1137/23m1598404","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1467-1510, September 2024. Abstract.We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their extended spatial range which makes them less sensitive to strictly local perturbations/modelling errors or the distance to the plume source. In contrast to other state-of-the-art DIAL methods, we do not make a single scattering assumption but rather propose a new type modality which includes the collection of multiply scattered photons from wider/multiple fields-of-view and argue that this data, paired with a time dependent radiative transfer model, is beneficial for the reconstruction of certain image features. The resulting inverse problem is solved by means of a semiparametric approach in which the image is reduced to a small number of dispersion related parameters and high-dimensional but computationally convenient nuisance component. This not only allows us to effectively avoid a high-dimensional inverse problem but simultaneously provides a natural regularization mechanism along with parameters which are directly related to the dispersion model. These can be associated with meaningful physical units while spatial concentration profiles can be obtained by means of forward evaluation of the dispersion process.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"43 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609697","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 Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis 矢量束上高斯混合物的瓦瑟斯坦型距离及其在形状分析中的应用

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-11 DOI: 10.1137/23m1620363

Michael Wilson, Tom Needham, Chiwoo Park, Suparteek Kundu, Anuj Srivastava

{"title":"A Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis","authors":"Michael Wilson, Tom Needham, Chiwoo Park, Suparteek Kundu, Anuj Srivastava","doi":"10.1137/23m1620363","DOIUrl":"https://doi.org/10.1137/23m1620363","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1433-1466, September 2024. Abstract.This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as mixtures of Gaussians on vector bundles and estimates the population parameters using a mode-based clustering algorithm. We derive a Wasserstein-type metric between Gaussian mixtures, adapted to the manifold geometry, in order to compare estimated distributions. Our contributions include an identifiability result for Gaussian mixtures on manifold domains and a convenient characterization of optimal couplings of Gaussian mixtures under the derived metric. We demonstrate these tools on some example domains, including the preshape space of planar closed curves, with applications to the shape space of triangles and populations of nanoparticles. In the nanoparticle application, we consider a sequence of populations of particle shapes arising from a manufacturing process and utilize the Wasserstein-type distance to perform change-point detection.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"62 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609696","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

Fast Certifiable Algorithm for the Absolute Pose Estimation of a Camera 相机绝对姿态估计的快速可认证算法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-11 DOI: 10.1137/23m159994x

Mercedes Garcia-Salguero, Elijs Dima, André Mateus, Javier Gonzalez-Jimenez

{"title":"Fast Certifiable Algorithm for the Absolute Pose Estimation of a Camera","authors":"Mercedes Garcia-Salguero, Elijs Dima, André Mateus, Javier Gonzalez-Jimenez","doi":"10.1137/23m159994x","DOIUrl":"https://doi.org/10.1137/23m159994x","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1415-1432, September 2024. Abstract.Estimating the absolute pose of a camera given a set of [math] points and their observations is known as the resectioning or Perspective-n-Point (PnP) problem. It is at the core of most computer vision applications and it can be stated as an instance of three-dimensional registration with point-line distances, making the error quadratic in the unknown pose. The PnP problem, though, is nonconvex due to the constraints associated with the rotation, and iterative algorithms may get trapped into any suboptimal solutions without notice. This work proposes an efficient certification algorithm for central and noncentral cameras that either confirms the optimality of a solution or is inconclusive. We exploit different sets of constraints for the rotation to assess their performance in terms of certification. Two of the formulations lack the Linear Independence Constraint Qualification (LICQ) while one of them has more constraints than variables. This hinders the usage of the “standard” procedure which estimates the Lagrange multipliers in closed-form. To overcome that, we formulate the certification as an eigenvalue optimization and solve it through a line-search method. Our evaluation on synthetic and real data shows that minimal formulations certify most solutions (more than [math] on real data) whereas redundant formulations are able to certify all of them and even random problem instances. The proposed algorithm runs in microseconds for all these formulations.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"108 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609720","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

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D 通过在一个观测点和稀疏观测点测量的多频数据对移动点源进行成像（第二部分）：三维近场案例

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-03 DOI: 10.1137/23m162260x

Guanqiu Ma, Hongxia Guo, Guanghui Hu

{"title":"Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D","authors":"Guanqiu Ma, Hongxia Guo, Guanghui Hu","doi":"10.1137/23m162260x","DOIUrl":"https://doi.org/10.1137/23m162260x","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1377-1414, September 2024. Abstract.In this paper, we introduce a frequency-domain approach to extract information on the trajectory of a moving point source. The method hinges on the analysis of multifrequency near-field data recorded at one and sparse observation points in three dimensions. The radiating period of the moving point source is supposed to be supported on the real axis and a priori known. In contrast to inverse stationary source problems, one needs to classify observable and non-observable measurement positions. The analogues of these concepts in the far-field regime were first proposed in the authors’ previous paper [SIAM J. Imaging Sci., 16 (2023), pp. 1535–1571]. In this paper we shall derive the observable and non-observable measurement positions for straight and circular motions in [math]. In the near-field case, we verify that the smallest annular region centered at an observable position that contains the trajectory can be imaged for an admissible class of orbit functions. Using the data from sparse observable positions, it is possible to reconstruct the [math]-convex domain of the trajectory. Intensive 3D numerical tests with synthetic data are performed to show effectiveness and feasibility of this new algorithm.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551083","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

IML FISTA: A Multilevel Framework for Inexact and Inertial Forward-Backward. Application to Image Restoration IML FISTA：不精确和惯性前向-后向的多层次框架。应用于图像复原

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-07-01 DOI: 10.1137/23m1582345

Guillaume Lauga, Elisa Riccietti, Nelly Pustelnik, Paulo Gonçalves

引用次数: 0