Pub Date : 2024-06-11DOI: 10.1088/1361-6420/ad4dda
Yan Chang, Yukun Guo, Hongyu Liu and Deyue Zhang
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier–Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method.
{"title":"A novel Newton method for inverse elastic scattering problems","authors":"Yan Chang, Yukun Guo, Hongyu Liu and Deyue Zhang","doi":"10.1088/1361-6420/ad4dda","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4dda","url":null,"abstract":"This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier–Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"205 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-10DOI: 10.1088/1361-6420/ad4f0b
Kai Li, Bo Zhang, Haiwen Zhang
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear), and certain regularization strategy is thus needed. However, it is difficult to select an appropriate regularization strategy which should enforce some a priori information of the unknown scatterer. To address this issue, we plan to use a deep learning approach to learn some a priori information of the unknown scatterer from certain ground truth data, which is then combined with a traditional iteration method to solve the inverse problem. Specifically, we propose a deep learning-based iterative reconstruction algorithm for the inverse problem, based on a repeated application of a deep neural network and the iteratively regularized Gauss–Newton method (IRGNM). Our deep neural network (called the learned projector in this paper) mainly focuses on learning the a priori information of the shape of the unknown contrast with a normalization technique in the training processes and is trained to act like a projector which is helpful for projecting the solution into some feasible region. Extensive numerical experiments show that our reconstruction algorithm provides good reconstruction results even for the high contrast case and has a satisfactory generalization ability.
{"title":"Reconstruction of inhomogeneous media by an iteration algorithm with a learned projector","authors":"Kai Li, Bo Zhang, Haiwen Zhang","doi":"10.1088/1361-6420/ad4f0b","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4f0b","url":null,"abstract":"This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear), and certain regularization strategy is thus needed. However, it is difficult to select an appropriate regularization strategy which should enforce some <italic toggle=\"yes\">a priori</italic> information of the unknown scatterer. To address this issue, we plan to use a deep learning approach to learn some <italic toggle=\"yes\">a priori</italic> information of the unknown scatterer from certain ground truth data, which is then combined with a traditional iteration method to solve the inverse problem. Specifically, we propose a deep learning-based iterative reconstruction algorithm for the inverse problem, based on a repeated application of a deep neural network and the iteratively regularized Gauss–Newton method (IRGNM). Our deep neural network (called the learned projector in this paper) mainly focuses on learning the <italic toggle=\"yes\">a priori</italic> information of the <italic toggle=\"yes\">shape</italic> of the unknown contrast with a normalization technique in the training processes and is trained to act like a projector which is helpful for projecting the solution into some feasible region. Extensive numerical experiments show that our reconstruction algorithm provides good reconstruction results even for the high contrast case and has a satisfactory generalization ability.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"63 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-03DOI: 10.1088/1361-6420/ad4669
Bjørn Jensen, Adrian Kirkeby and Kim Knudsen
In acousto-electric tomography (AET) the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is perturbed by a time-dependent acoustic wave, thus taking advantage of the acousto-electric effect. We approach the AET reconstruction in two steps: First, the interior power density is obtained from boundary measurements by solving a linear inverse and ill-posed problem; second, the interior conductivity is reconstructed from the power density by solving a non-linear and well-posed problem. Mathematically these inverse problems are fairly well understood, and reconstruction methods work well on synthetic data. This is in contrast to experimental findings. An effect can indeed be observed and data can be collected. However, the acousto-electric coupling is very weak, and consequently, the change in the measured voltage due to the acoustic perturbation might be too small compared to the background noise for viable reconstructions. In this paper, we take one step towards understanding the feasibility of AET. We provide an in-silico model of the coupled physics scenario based on standard models for the individual phenomena. Moreover, we formulate and implement numerically a full reconstruction method for the inverse problem via the two steps. We perform computational experiments with realistically chosen parameters from the context of medical imaging. The focus is on understanding the role of the acousto-electric coupling parameter and the signal-to-noise ratio (SNR). The critical signal strength is analyzed and the omnipresent Johnson–Nyquist noise is estimated. We obtain both positive and negative findings; we can reconstruct features even under severe noise conditions, but we also find that the SNR one is likely to face in practice is too low to obtain useful reconstructions.
声电层析成像（AET）的目标是通过对相应电流和电压的静电边界测量重建域中的电导率，同时域受到随时间变化的声波扰动，从而利用声电效应。我们分两步进行 AET 重建：首先，通过求解一个线性反问题和求解困难的问题，从边界测量中获得内部功率密度；其次，通过求解一个非线性和求解困难的问题，从功率密度中重建内部传导性。从数学角度来看，这些逆问题都相当容易理解，而且重建方法在合成数据上也很有效。这与实验结果截然不同。确实可以观察到效果，也可以收集数据。然而，声电耦合非常微弱，因此，与背景噪声相比，声学扰动引起的测量电压变化可能太小，无法进行可行的重建。在本文中，我们朝着了解 AET 的可行性迈出了一步。我们基于单个现象的标准模型，提供了一个耦合物理场景的内部模型。此外，我们通过两个步骤为逆问题制定并数值化了一个完整的重建方法。我们使用医学成像中实际选择的参数进行了计算实验。重点是了解声电耦合参数和信噪比（SNR）的作用。我们分析了临界信号强度，并估算了无处不在的约翰逊-奈奎斯特噪声。我们得出了正反两方面的结论：即使在严重的噪声条件下，我们也能重建特征，但我们也发现，在实践中可能面临的信噪比太低，无法获得有用的重建。
{"title":"Feasibility of acousto-electric tomography","authors":"Bjørn Jensen, Adrian Kirkeby and Kim Knudsen","doi":"10.1088/1361-6420/ad4669","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4669","url":null,"abstract":"In acousto-electric tomography (AET) the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is perturbed by a time-dependent acoustic wave, thus taking advantage of the acousto-electric effect. We approach the AET reconstruction in two steps: First, the interior power density is obtained from boundary measurements by solving a linear inverse and ill-posed problem; second, the interior conductivity is reconstructed from the power density by solving a non-linear and well-posed problem. Mathematically these inverse problems are fairly well understood, and reconstruction methods work well on synthetic data. This is in contrast to experimental findings. An effect can indeed be observed and data can be collected. However, the acousto-electric coupling is very weak, and consequently, the change in the measured voltage due to the acoustic perturbation might be too small compared to the background noise for viable reconstructions. In this paper, we take one step towards understanding the feasibility of AET. We provide an in-silico model of the coupled physics scenario based on standard models for the individual phenomena. Moreover, we formulate and implement numerically a full reconstruction method for the inverse problem via the two steps. We perform computational experiments with realistically chosen parameters from the context of medical imaging. The focus is on understanding the role of the acousto-electric coupling parameter and the signal-to-noise ratio (SNR). The critical signal strength is analyzed and the omnipresent Johnson–Nyquist noise is estimated. We obtain both positive and negative findings; we can reconstruct features even under severe noise conditions, but we also find that the SNR one is likely to face in practice is too low to obtain useful reconstructions.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-29eCollection Date: 2024-01-01DOI: 10.29399/npa.28443
Ülker Atılan Fedai, Halil Fedai
Introduction: Electroconvulsive therapy (ECT) is one of the biological therapies that is well tolerated and has a low risk of complications. Acute cardiovascular complications related to ECT such as ventricular arrhythmia, myocardial infarction and cardiac arrest have been recorded. Increased frontal QRS-T (fQRS-T) angle was associated with ventricular arrhythmia, sudden cardiac death and total mortality. In this study, we aimed to evaluate the effect of ECT on the myocardium using electrocardiography (ECG) parameters such as fQRS-T angle, QRS duration, QT and QTc interval.
Methods: A total of 108 patients diagnosed with bipolar disorder (n=36), depressive disorder (n=70) and schizophrenia (n=2) who underwent ECT were included in this study. 12-lead surface ECG of all patients were taken before the ECT, 15 min. after ECT and 24 hour after ECT.
Results: QRS duration, QT interval and corrected QT (QTc) interval were not changed significantly during the follow-up period. However, we found that, fQRS-T angle was significantly increased 15 minutes after ECT compared to baseline angle (p<0.001). We also detected that this increase in fQRS-T angle 15 minutes after ECT was significantly reduced 24 hours after ECT (p=0.031). Meanwhile, there was no significant difference between baseline and 24th hour fQRS-T angle (p=0.154).
Conclusions: In our study, a significant increase in fQRS-T angle was observed 15 min after ECT. However, the fQRS-T angle was found to return to normal after 24 hours. Our findings may indicate that ECT does not have a permanent side effect on the risk of cardiovascular events according to the fQRS-T angle.
{"title":"The Effect of Electroconvulsive Therapy on Frontal QRS-T Angle in Psychiatric Patients.","authors":"Ülker Atılan Fedai, Halil Fedai","doi":"10.29399/npa.28443","DOIUrl":"10.29399/npa.28443","url":null,"abstract":"<p><strong>Introduction: </strong>Electroconvulsive therapy (ECT) is one of the biological therapies that is well tolerated and has a low risk of complications. Acute cardiovascular complications related to ECT such as ventricular arrhythmia, myocardial infarction and cardiac arrest have been recorded. Increased frontal QRS-T (fQRS-T) angle was associated with ventricular arrhythmia, sudden cardiac death and total mortality. In this study, we aimed to evaluate the effect of ECT on the myocardium using electrocardiography (ECG) parameters such as fQRS-T angle, QRS duration, QT and QTc interval.</p><p><strong>Methods: </strong>A total of 108 patients diagnosed with bipolar disorder (n=36), depressive disorder (n=70) and schizophrenia (n=2) who underwent ECT were included in this study. 12-lead surface ECG of all patients were taken before the ECT, 15 min. after ECT and 24 hour after ECT.</p><p><strong>Results: </strong>QRS duration, QT interval and corrected QT (QTc) interval were not changed significantly during the follow-up period. However, we found that, fQRS-T angle was significantly increased 15 minutes after ECT compared to baseline angle (p<0.001). We also detected that this increase in fQRS-T angle 15 minutes after ECT was significantly reduced 24 hours after ECT (p=0.031). Meanwhile, there was no significant difference between baseline and 24th hour fQRS-T angle (p=0.154).</p><p><strong>Conclusions: </strong>In our study, a significant increase in fQRS-T angle was observed 15 min after ECT. However, the fQRS-T angle was found to return to normal after 24 hours. Our findings may indicate that ECT does not have a permanent side effect on the risk of cardiovascular events according to the fQRS-T angle.</p>","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"27 1","pages":"135-140"},"PeriodicalIF":1.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11165600/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82794533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1088/1361-6420/ad49cc
Hiroshi Fujiwara, David Omogbhe, Kamran Sadiq and Alexandru Tamasan
We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim’s A-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of one-tensors.
{"title":"Inversion of the attenuated momenta ray transform of planar symmetric tensors","authors":"Hiroshi Fujiwara, David Omogbhe, Kamran Sadiq and Alexandru Tamasan","doi":"10.1088/1361-6420/ad49cc","DOIUrl":"https://doi.org/10.1088/1361-6420/ad49cc","url":null,"abstract":"We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim’s A-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of one-tensors.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"63 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1088/1361-6420/ad49cd
Song-Ren Fu, Peng-Fei Yao and Yongyi Yu
This paper is devoted to some inverse problems of recovering the nonlinearity for the Jordan–Moore–Gibson–Thompson equation, which is a third order nonlinear acoustic equation. This equation arises, for example, from the wave propagation in viscous thermally relaxing fluids. The well-posedness of the nonlinear equation is obtained with the small initial and boundary data. By the second order linearization to the nonlinear equation, and construction of complex geometric optics solutions for the linearized equation, the uniqueness of recovering the nonlinearity is derived.
{"title":"Inverse problem of recovering a time-dependent nonlinearity appearing in third-order nonlinear acoustic equations *","authors":"Song-Ren Fu, Peng-Fei Yao and Yongyi Yu","doi":"10.1088/1361-6420/ad49cd","DOIUrl":"https://doi.org/10.1088/1361-6420/ad49cd","url":null,"abstract":"This paper is devoted to some inverse problems of recovering the nonlinearity for the Jordan–Moore–Gibson–Thompson equation, which is a third order nonlinear acoustic equation. This equation arises, for example, from the wave propagation in viscous thermally relaxing fluids. The well-posedness of the nonlinear equation is obtained with the small initial and boundary data. By the second order linearization to the nonlinear equation, and construction of complex geometric optics solutions for the linearized equation, the uniqueness of recovering the nonlinearity is derived.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"67 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1088/1361-6420/ad4911
Ashwin Tarikere and Hanming Zhou
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.
{"title":"Stability and statistical inversion of travel time tomography","authors":"Ashwin Tarikere and Hanming Zhou","doi":"10.1088/1361-6420/ad4911","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4911","url":null,"abstract":"In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"91 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.1088/1361-6420/ad466a
Junqing Chen, Bangti Jin and Haibo Liu
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of an obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse problem, we advocate the use of a trained latent representation of surfaces as the generative prior. This prior enjoys excellent expressivity within the given class of shapes, and meanwhile, the latent dimensionality is low, which greatly facilitates the computation. Thus, the admissible manifold of surfaces is realistic and the resulting optimization problem is less ill-posed. We employ the shape derivative to evolve the latent surface representation, by minimizing the loss, and we provide a local convergence analysis of a gradient descent type algorithm to a stationary point of the loss. We present several numerical examples, including also backscattered and phaseless data, to showcase the effectiveness of the proposed algorithm.
{"title":"Solving inverse obstacle scattering problem with latent surface representations","authors":"Junqing Chen, Bangti Jin and Haibo Liu","doi":"10.1088/1361-6420/ad466a","DOIUrl":"https://doi.org/10.1088/1361-6420/ad466a","url":null,"abstract":"We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of an obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse problem, we advocate the use of a trained latent representation of surfaces as the generative prior. This prior enjoys excellent expressivity within the given class of shapes, and meanwhile, the latent dimensionality is low, which greatly facilitates the computation. Thus, the admissible manifold of surfaces is realistic and the resulting optimization problem is less ill-posed. We employ the shape derivative to evolve the latent surface representation, by minimizing the loss, and we provide a local convergence analysis of a gradient descent type algorithm to a stationary point of the loss. We present several numerical examples, including also backscattered and phaseless data, to showcase the effectiveness of the proposed algorithm.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"43 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-25DOI: 10.1088/1361-6420/ad3eaa
Manuel Cañizares
The focus of this paper is the study of the inverse point-source scattering problem, specifically in relation to a certain class of electric potentials. Our research provides a novel uniqueness result for the inverse problem with local data, obtained from the near field pattern. Our work improves the work of Caro and Garcia, who investigated both the direct problem and the inverse problem with global near field data for critically singular and -shell potentials. The primary contribution of our research is the introduction of a Runge approximation result for the near field data on the scattering problem which, in combination with an interior regularity argument, enables us to establish a uniqueness result for the inverse problem with local data. Additionaly, we manage to consider a slightly wider class of potentials.
本文的重点是研究逆点源散射问题，特别是与某类电势有关的问题。我们的研究为反问题提供了一个新的唯一性结果，该结果具有从近场模式获得的局部数据。我们的工作改进了 Caro 和 Garcia 的工作，他们研究了临界奇异和壳势的直接问题和具有全局近场数据的逆问题。我们研究的主要贡献是引入了散射问题近场数据的 Runge 近似结果，结合内部正则性论证，使我们能够为具有局部数据的逆问题建立唯一性结果。此外，我们还设法考虑了更广泛的势。
{"title":"Local near-field scattering data enables unique reconstruction of rough electric potentials","authors":"Manuel Cañizares","doi":"10.1088/1361-6420/ad3eaa","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3eaa","url":null,"abstract":"The focus of this paper is the study of the inverse point-source scattering problem, specifically in relation to a certain class of electric potentials. Our research provides a novel uniqueness result for the inverse problem with local data, obtained from the near field pattern. Our work improves the work of Caro and Garcia, who investigated both the direct problem and the inverse problem with global near field data for critically singular and -shell potentials. The primary contribution of our research is the introduction of a Runge approximation result for the near field data on the scattering problem which, in combination with an interior regularity argument, enables us to establish a uniqueness result for the inverse problem with local data. Additionaly, we manage to consider a slightly wider class of potentials.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-23DOI: 10.1088/1361-6420/ad3c67
Julien Ajdenbaum, Emilie Chouzenoux, Claire Lefort, Ségolène Martin and Jean-Christophe Pesquet
In multi-photon microscopy (MPM), a recent in-vivo fluorescence microscopy system, the task of image restoration can be decomposed into two interlinked inverse problems: firstly, the characterization of the point spread function (PSF) and subsequently, the deconvolution (i.e. deblurring) to remove the PSF effect, and reduce noise. The acquired MPM image quality is critically affected by PSF blurring and intense noise. The PSF in MPM is highly spread in 3D and is not well characterized, presenting high variability with respect to the observed objects. This makes the restoration of MPM images challenging. Common PSF estimation methods in fluorescence microscopy, including MPM, involve capturing images of sub-resolution beads, followed by quantifying the resulting ellipsoidal 3D spot. In this work, we revisit this approach, coping with its inherent limitations in terms of accuracy and practicality. We estimate the PSF from the observation of relatively large beads (approximately 1 in diameter). This goes through the formulation and resolution of an original non-convex minimization problem, for which we propose a proximal alternating method along with convergence guarantees. Following the PSF estimation step, we then introduce an innovative strategy to deal with the high level multiplicative noise degrading the acquisitions. We rely on a heteroscedastic noise model for which we estimate the parameters. We then solve a constrained optimization problem to restore the image, accounting for the estimated PSF and noise, while allowing a minimal hyper-parameter tuning. Theoretical guarantees are given for the restoration algorithm. These algorithmic contributions lead to an end-to-end pipeline for 3D image restoration in MPM, that we share as a publicly available Python software. We demonstrate its effectiveness through several experiments on both simulated and real data.
{"title":"A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution","authors":"Julien Ajdenbaum, Emilie Chouzenoux, Claire Lefort, Ségolène Martin and Jean-Christophe Pesquet","doi":"10.1088/1361-6420/ad3c67","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3c67","url":null,"abstract":"In multi-photon microscopy (MPM), a recent in-vivo fluorescence microscopy system, the task of image restoration can be decomposed into two interlinked inverse problems: firstly, the characterization of the point spread function (PSF) and subsequently, the deconvolution (i.e. deblurring) to remove the PSF effect, and reduce noise. The acquired MPM image quality is critically affected by PSF blurring and intense noise. The PSF in MPM is highly spread in 3D and is not well characterized, presenting high variability with respect to the observed objects. This makes the restoration of MPM images challenging. Common PSF estimation methods in fluorescence microscopy, including MPM, involve capturing images of sub-resolution beads, followed by quantifying the resulting ellipsoidal 3D spot. In this work, we revisit this approach, coping with its inherent limitations in terms of accuracy and practicality. We estimate the PSF from the observation of relatively large beads (approximately 1 in diameter). This goes through the formulation and resolution of an original non-convex minimization problem, for which we propose a proximal alternating method along with convergence guarantees. Following the PSF estimation step, we then introduce an innovative strategy to deal with the high level multiplicative noise degrading the acquisitions. We rely on a heteroscedastic noise model for which we estimate the parameters. We then solve a constrained optimization problem to restore the image, accounting for the estimated PSF and noise, while allowing a minimal hyper-parameter tuning. Theoretical guarantees are given for the restoration algorithm. These algorithmic contributions lead to an end-to-end pipeline for 3D image restoration in MPM, that we share as a publicly available Python software. We demonstrate its effectiveness through several experiments on both simulated and real data.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","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：