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

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

Training Adaptive Reconstruction Networks for Blind Inverse Problems 为盲反问题训练自适应重构网络

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-21 DOI: 10.1137/23m1545628

Alban Gossard, Pierre Weiss

引用次数: 0

Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on Surfaces 用于曲面图像去噪的非 Lipschitz 变分模型及其迭代加权最小二乘法算法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-20 DOI: 10.1137/23m159439x

Yuan Liu, Chunlin Wu, Chao Zeng

引用次数: 0

Riesz Feature Representation: Scale Equivariant Scattering Network for Classification Tasks 里兹特征表示：用于分类任务的尺度等变散射网络

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-20 DOI: 10.1137/23m1584836

Tin Barisin, Jesus Angulo, Katja Schladitz, Claudia Redenbach

{"title":"Riesz Feature Representation: Scale Equivariant Scattering Network for Classification Tasks","authors":"Tin Barisin, Jesus Angulo, Katja Schladitz, Claudia Redenbach","doi":"10.1137/23m1584836","DOIUrl":"https://doi.org/10.1137/23m1584836","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1284-1313, June 2024. Abstract. Scattering networks yield powerful and robust hierarchical image descriptors which do not require lengthy training and which work well with very few training data. However, they rely on sampling the scale dimension. Hence, they become sensitive to scale variations and are unable to generalize to unseen scales. In this work, we define an alternative feature representation based on the Riesz transform. We detail and analyze the mathematical foundations behind this representation. In particular, it inherits scale equivariance from the Riesz transform and completely avoids sampling of the scale dimension. Additionally, the number of features in the representation is reduced by a factor four compared to scattering networks. Nevertheless, our representation performs comparably well for texture classification with an interesting addition: scale equivariance. Our method yields very good performance when dealing with scales outside of those covered by the training dataset. The usefulness of the equivariance property is demonstrated on the digit classification task, where accuracy remains stable even for scales four times larger than the one chosen for training. As a second example, we consider classification of textures. Finally, we show how this representation can be used to build hybrid deep learning methods that are more stable to scale variations than standard deep networks.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"111 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529027","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

Marginal Likelihood Estimation in Semiblind Image Deconvolution: A Stochastic Approximation Approach 半盲图像解卷积中的边际似然估计：随机逼近法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-19 DOI: 10.1137/23m1584496

Charlesquin Kemajou Mbakam, Marcelo Pereyra, Jean-François Giovannelli

{"title":"Marginal Likelihood Estimation in Semiblind Image Deconvolution: A Stochastic Approximation Approach","authors":"Charlesquin Kemajou Mbakam, Marcelo Pereyra, Jean-François Giovannelli","doi":"10.1137/23m1584496","DOIUrl":"https://doi.org/10.1137/23m1584496","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1206-1254, June 2024. Abstract.This paper presents a novel stochastic optimization methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed optimization approach automatically calibrates the parameters of the blur model by maximum marginal likelihood estimation, followed by (non-blind) image deconvolution by maximum a posteriori estimation conditionally to the estimated model parameters. In addition to the blur model, the proposed approach also automatically calibrates the noise level as well as any regularization parameters. The marginal likelihood of the blur, noise, and regularization parameters is generally computationally intractable, as it requires calculating several integrals over the entire solution space. Our approach addresses this difficulty by using a stochastic approximation proximal gradient optimization scheme, which iteratively solves such integrals by using a Moreau–Yosida regularized unadjusted Langevin Markov chain Monte Carlo algorithm. This optimization strategy can be easily and efficiently applied to any model that is log-concave and by using the same gradient and proximal operators that are required to compute the maximum a posteriori solution by convex optimization. We provide convergence guarantees for the proposed optimization scheme under realistic and easily verifiable conditions and subsequently demonstrate the effectiveness of the approach with a series of deconvolution experiments and comparisons with alternative strategies from the state of the art","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"8 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503739","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