Let and , , be real numbers. We show by an example that the assignment problem begin{align*} max_{sigma in S_n} F_sigma (x,y) := frac 12 sum_{i,k=1}^n |x_i- x_k|^alpha , |y_{sigma (i)}- y_{sigma (k)}|^alpha, quad alpha gt 0, end{align*} is in general neither solved by the identical permutation nor the anti-identical permutation if . Indeed the above maximum can be, depending on the number of points, arbitrarily far away from and . The motivation to deal with such assignment problems came from their relation to Gromov–Wasserstein distances, which have recently received a lot of attention in imaging and shape analysis.
{"title":"On Assignment Problems Related to Gromov–Wasserstein Distances on the Real Line","authors":"Robert Beinert, Cosmas Heiss, Gabriele Steidl","doi":"10.1137/22m1497808","DOIUrl":"https://doi.org/10.1137/22m1497808","url":null,"abstract":"Let and , , be real numbers. We show by an example that the assignment problem begin{align*} max_{sigma in S_n} F_sigma (x,y) := frac 12 sum_{i,k=1}^n |x_i- x_k|^alpha , |y_{sigma (i)}- y_{sigma (k)}|^alpha, quad alpha gt 0, end{align*} is in general neither solved by the identical permutation nor the anti-identical permutation if . Indeed the above maximum can be, depending on the number of points, arbitrarily far away from and . The motivation to deal with such assignment problems came from their relation to Gromov–Wasserstein distances, which have recently received a lot of attention in imaging and shape analysis.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135903434","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}
Tamir Bendory, Nicolas Boumal, William Leeb, Eitan Levin, Amit Singer
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.
{"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":"17 1","pages":"0"},"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}
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.
{"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":"33 1","pages":"0"},"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}
In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimization methods in machine learning, imaging, and signal processing, to name a few. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularizing property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach.
{"title":"On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces","authors":"Bangti Jin, Željko Kereta","doi":"10.1137/22m1518542","DOIUrl":"https://doi.org/10.1137/22m1518542","url":null,"abstract":"In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimization methods in machine learning, imaging, and signal processing, to name a few. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularizing property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134959861","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}
This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as a nonlocal reparametrization of the assignment flow approach that was introduced in [J. Math. Imaging Vision, 58 (2017), pp. 211–238]. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with respect to a nonconvex potential. We devise an entropy-regularized difference of convex (DC) functions decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments.
{"title":"A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling","authors":"Dmitrij Sitenko, Bastian Boll, Christoph Schnörr","doi":"10.1137/22m1496141","DOIUrl":"https://doi.org/10.1137/22m1496141","url":null,"abstract":"This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as a nonlocal reparametrization of the assignment flow approach that was introduced in [J. Math. Imaging Vision, 58 (2017), pp. 211–238]. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with respect to a nonconvex potential. We devise an entropy-regularized difference of convex (DC) functions decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"444 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136001736","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}
Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski
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.
{"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":"243 1","pages":"0"},"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}
Fabian Hinterer, Simon Hubmer, Prashin Jethwa, Kirk M. Soodhalter, Glenn van de Ven, Ronny Ramlau
In this paper, we consider the problem of reconstructing a galaxy’s stellar population-kinematic distribution function from optical integral field unit measurements. These quantities are connected via a high-dimensional integral equation. To solve this problem, we propose a projected Nesterov–Kaczmarz reconstruction method, which efficiently leverages the problem structure and incorporates physical prior information such as smoothness and nonnegativity constraints. To test the performance of our reconstruction approach, we apply it to a dataset simulated from a known ground truth density, and validate it by comparing our recoveries to those obtained by the widely used pPXF software.
{"title":"A Projected Nesterov–Kaczmarz Approach to Stellar Population-Kinematic Distribution Reconstruction in Extragalactic Archaeology","authors":"Fabian Hinterer, Simon Hubmer, Prashin Jethwa, Kirk M. Soodhalter, Glenn van de Ven, Ronny Ramlau","doi":"10.1137/22m1503002","DOIUrl":"https://doi.org/10.1137/22m1503002","url":null,"abstract":"In this paper, we consider the problem of reconstructing a galaxy’s stellar population-kinematic distribution function from optical integral field unit measurements. These quantities are connected via a high-dimensional integral equation. To solve this problem, we propose a projected Nesterov–Kaczmarz reconstruction method, which efficiently leverages the problem structure and incorporates physical prior information such as smoothness and nonnegativity constraints. To test the performance of our reconstruction approach, we apply it to a dataset simulated from a known ground truth density, and validate it by comparing our recoveries to those obtained by the widely used pPXF software.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136181814","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}
Andreas Alpers, Maximilian Fiedler, Peter Gritzmann, Fabian Klemm
The present paper studies mathematical models for representing, imaging, and analyzing polycrystalline materials. We introduce various techniques for converting grain maps into diagram or tessellation representations that rely on constrained clustering. In particular, we show how to significantly accelerate the computation of generalized balanced power diagrams and how to extend it to allow for optimization over all relevant parameters. A comparison of the accuracy of the proposed approaches is given based on a three-dimensional real-world data set of voxels.
{"title":"Turning Grain Maps into Diagrams","authors":"Andreas Alpers, Maximilian Fiedler, Peter Gritzmann, Fabian Klemm","doi":"10.1137/22m1491988","DOIUrl":"https://doi.org/10.1137/22m1491988","url":null,"abstract":"The present paper studies mathematical models for representing, imaging, and analyzing polycrystalline materials. We introduce various techniques for converting grain maps into diagram or tessellation representations that rely on constrained clustering. In particular, we show how to significantly accelerate the computation of generalized balanced power diagrams and how to extend it to allow for optimization over all relevant parameters. A comparison of the accuracy of the proposed approaches is given based on a three-dimensional real-world data set of voxels.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136180941","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}
Pub Date : 2022-01-01Epub Date: 2022-05-26DOI: 10.1137/21m143529x
Tommy M Tang, Hemant D Tagare
Steerable filter pairs that are near quadrature have many image processing applications. This paper proposes a new methodology for designing such filters. The key idea is to design steerable filters by minimizing a departure-from-quadrature function. These minimizing filter pairs are almost exactly in quadrature. The polar part of the filters is nonnegative, monotonic, and highly focused around an axis, and asymptotically the filters achieve exact quadrature. These results are established by exploiting a relation between the filters and generalized Hilbert matrices. These near-quadrature filters closely approximate three dimensional Gabor filters. We experimentally verify the asymptotic mathematical results and further demonstrate the use of these filter pairs by efficient calculation of local Fourier shell correlation of cryogenic electron microscopy.
{"title":"Steerable Near-Quadrature Filter Pairs in Three Dimensions.","authors":"Tommy M Tang, Hemant D Tagare","doi":"10.1137/21m143529x","DOIUrl":"https://doi.org/10.1137/21m143529x","url":null,"abstract":"<p><p>Steerable filter pairs that are near quadrature have many image processing applications. This paper proposes a new methodology for designing such filters. The key idea is to design steerable filters by minimizing a departure-from-quadrature function. These minimizing filter pairs are almost exactly in quadrature. The polar part of the filters is nonnegative, monotonic, and highly focused around an axis, and asymptotically the filters achieve exact quadrature. These results are established by exploiting a relation between the filters and generalized Hilbert matrices. These near-quadrature filters closely approximate three dimensional Gabor filters. We experimentally verify the asymptotic mathematical results and further demonstrate the use of these filter pairs by efficient calculation of local Fourier shell correlation of cryogenic electron microscopy.</p>","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"15 2","pages":"670-700"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9683347/pdf/nihms-1847751.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40704943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Linh Nguyen, Markus Haltmeier, Richard Kowar, Ngoc Do
Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT measurement setup, the used data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique provide the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known for the full field PAT problem. In this paper, we build mathematical foundations of the latter problem for variable sound speed and settle its uniqueness and stability. Moreover, we introduce an exact inversion method using time-reversal and study its convergence. Our results demonstrate the suitability of both the full field approach and the proposed time-reversal technique for high resolution photoacoustic imaging.
{"title":"Analysis for Full-Field Photoacoustic Tomography with Variable Sound Speed.","authors":"Linh Nguyen, Markus Haltmeier, Richard Kowar, Ngoc Do","doi":"10.1137/21m1463409","DOIUrl":"10.1137/21m1463409","url":null,"abstract":"<p><p>Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT measurement setup, the used data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique provide the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known for the full field PAT problem. In this paper, we build mathematical foundations of the latter problem for variable sound speed and settle its uniqueness and stability. Moreover, we introduce an exact inversion method using time-reversal and study its convergence. Our results demonstrate the suitability of both the full field approach and the proposed time-reversal technique for high resolution photoacoustic imaging.</p>","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"15 3","pages":"1213-1228"},"PeriodicalIF":2.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10162777/pdf/nihms-1887591.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9437974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：