SIAM Journal on Imaging Sciences最新文献_第9页

Image Recovery for Blind Polychromatic Ptychography 盲多色印刷的图像恢复

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-07-28 DOI: 10.1137/22m1527155

Frank Filbir, Oleh Melnyk

引用次数: 0

Separable Quaternion Matrix Factorization for Polarization Images 偏振图像的可分离四元数矩阵分解

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-07-26 DOI: 10.1137/22m151248x

Junjun Pan, Michael K. Ng

{"title":"Separable Quaternion Matrix Factorization for Polarization Images","authors":"Junjun Pan, Michael K. Ng","doi":"10.1137/22m151248x","DOIUrl":"https://doi.org/10.1137/22m151248x","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1281-1307, September 2023. <br/> Abstract. A transverse wave is a wave in which the particles are displaced perpendicular to the direction of the wave’s advance. Examples of transverse waves include ripples on the surface of water and light waves. Polarization is one of the primary properties of transverse waves. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion linear mixing model for polarized signals: we assume each column of the source factor matrix equals a column of the polarized data matrix and refer to the corresponding problem as separable quaternion matrix factorization (SQMF). We discuss some properties of the matrix that can be decomposed by SQMF. To determine the source factor matrix in quaternion space, we propose a heuristic algorithm called quaternion successive projection algorithm (QSPA) inspired by the successive projection algorithm. To guarantee the effectiveness of QSPA, a new normalization operator is proposed for the quaternion matrix. We use a block coordinate descent algorithm to compute nonnegative activation matrix in real number space. We test our method on the applications of polarization image representation and spectro-polarimetric imaging unmixing to verify its effectiveness.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528997","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

Provable Phase Retrieval with Mirror Descent 可证明的相位反演与镜像下降

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-07-14 DOI: 10.1137/22m1528896

Jean-Jacques Godeme, Jalal Fadili, Xavier Buet, Myriam Zerrad, Michel Lequime, Claude Amra

{"title":"Provable Phase Retrieval with Mirror Descent","authors":"Jean-Jacques Godeme, Jalal Fadili, Xavier Buet, Myriam Zerrad, Michel Lequime, Claude Amra","doi":"10.1137/22m1528896","DOIUrl":"https://doi.org/10.1137/22m1528896","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1106-1141, September 2023. <br/> Abstract. In this paper, we consider the problem of phase retrieval, which consists of recovering an [math]‐dimensional real vector from the magnitude of its [math] linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm based on a wisely chosen Bregman divergence, hence allowing us to remove the classical global Lipschitz continuity requirement on the gradient of the nonconvex phase retrieval objective to be minimized. We apply the mirror descent for two random measurements: the i.i.d. standard Gaussian and those obtained by multiple structured illuminations through coded diffraction patterns. For the Gaussian case, we show that when the number of measurements [math] is large enough, then with high probability, for almost all initializers, the algorithm recovers the original vector up to a global sign change. For both measurements, the mirror descent exhibits a local linear convergence behavior with a dimension-independent convergence rate. Finally, our theoretical results are illustrated with various numerical experiments, including an application to the reconstruction of images in precision optics.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528998","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

On Assignment Problems Related to Gromov–Wasserstein Distances on the Real Line 实线上与Gromov-Wasserstein距离有关的分配问题

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-06-23 DOI: 10.1137/22m1497808

Robert Beinert, Cosmas Heiss, Gabriele Steidl

引用次数: 2

Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit 无粒子拾取的单粒子重构:突破检测极限

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-06-07 DOI: 10.1137/22m1503828

Tamir Bendory, Nicolas Boumal, William Leeb, Eitan Levin, Amit Singer

{"title":"Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit","authors":"Tamir Bendory, Nicolas Boumal, William Leeb, Eitan Levin, Amit Singer","doi":"10.1137/22m1503828","DOIUrl":"https://doi.org/10.1137/22m1503828","url":null,"abstract":"Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem, especially for small molecules. In this paper, we pursue a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. The aim is to bring small molecules within reach for cryo-EM. To this end, we design an autocorrelation analysis technique that allows one to go directly from the micrographs to the sought structures. This involves only one pass over the micrographs, allowing online, streaming processing for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a complementary approach to state-of-the-art algorithms.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135363967","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: 1

On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector 利用平面定向敏感探测器学习光声层析成像中的不可见性

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-05-18 DOI: 10.1137/22m148793x

Bolin Pan, Marta M. Betcke

{"title":"On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector","authors":"Bolin Pan, Marta M. Betcke","doi":"10.1137/22m148793x","DOIUrl":"https://doi.org/10.1137/22m148793x","url":null,"abstract":"In photoacoustic tomography (PAT) with a flat sensor, we routinely encounter two types of limited data. The first is due to using a finite sensor and is especially perceptible if the region of interest is large relative to the sensor or located farther away from the sensor. In this paper, we focus on the second type caused by a varying sensitivity of the sensor to the incoming wavefront direction, which can be modelled as binary, i.e., by a cone of sensitivity. Such visibility conditions result, in the Fourier domain, in a restriction of both the image and the data to a bowtie, akin to the one corresponding to the range of the forward operator. The visible wavefrontsets in image and data domains, are related by the wavefront direction mapping. We adapt the wedge restricted curvelet decomposition, we previously proposed for the representation of the full PAT data, to separate the visible and invisible wavefronts in the image. We optimally combine fast approximate operators with tailored deep neural network architectures into efficient learned reconstruction methods which perform reconstruction of the visible coefficients, and the invisible coefficients are learned from a training set of similar data.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135717995","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

On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces Banach空间中线性逆问题的随机梯度下降收敛性

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-05-15 DOI: 10.1137/22m1518542

Bangti Jin, Željko Kereta

引用次数: 0

Elastica Models for Color Image Regularization 彩色图像正则化的弹性模型

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-03-30 DOI: 10.1137/22m147935x

Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski

{"title":"Elastica Models for Color Image Regularization","authors":"Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski","doi":"10.1137/22m147935x","DOIUrl":"https://doi.org/10.1137/22m147935x","url":null,"abstract":"The choice of a proper regularization measure plays an important role in the field of image processing. One classical approach treats color images as two- dimensional surfaces embedded in a five-dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the chromatic coordinates as dominating over the spatial ones, we can think of the image spatial coordinates could as a parameterization of the image surface manifold in a three-dimensional color space. Minimizing the area of the image manifold leads to the Beltrami flow or mean curvature flow of the image surface in the three-dimensional color space, while minimizing the elastica of the image surface yields an additional interesting regularization. Recently, we proposed a color elastica model, which minimizes both the surface area and the elastica of the image manifold. In this paper, we propose to modify the color elastica and introduce two new models for color image regularization. The revised measures are motivated by the relations between the color elastica model, Euler’s elastica model, and the total variation model for gray level images. Compared to our previous color elastica model, the new models are direct extensions of Euler’s elastica model to color images. The proposed models are nonlinear and challenging to minimize. To overcome this difficulty, two operator-splitting methods are suggested. Specifically, nonlinearities are decoupled by the introduction of new vector- and matrix-valued variables. Then, the minimization problems are converted to initial value problems which are time-discretized by operator splitting. Each subproblem, after splitting, either has a closed-form solution or can be solved efficiently. The effectiveness and advantages of the proposed models are demonstrated by comprehensive experiments. The benefits of incorporating the elastica of the image surface as regularization terms compared to common alternatives are empirically validated.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136265878","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 Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling 图像标注的非局部图pde和高阶几何积分

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-03-30 DOI: 10.1137/22m1496141

Dmitrij Sitenko, Bastian Boll, Christoph Schnörr

引用次数: 1

A Projected Nesterov–Kaczmarz Approach to Stellar Population-Kinematic Distribution Reconstruction in Extragalactic Archaeology 基于Nesterov-Kaczmarz方法的河外考古中恒星人口运动分布重建

3区数学

SIAM Journal on Imaging Sciences Pub Date : 2023-02-07 DOI: 10.1137/22m1503002

Fabian Hinterer, Simon Hubmer, Prashin Jethwa, Kirk M. Soodhalter, Glenn van de Ven, Ronny Ramlau

引用次数: 2