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":null,"pages":null},"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":null,"pages":null},"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 : 2024-05-22DOI: 10.1088/1361-6420/ad4f0a
Refik Mert Çam, Umberto Villa, Mark A. Anastasio
Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as ``half-time" measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.
{"title":"Learning a stable approximation of an existing but unknown inverse mapping: Application to the half-time circular Radon transform","authors":"Refik Mert Çam, Umberto Villa, Mark A. Anastasio","doi":"10.1088/1361-6420/ad4f0a","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4f0a","url":null,"abstract":"\u0000 Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as ``half-time\" measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141110224","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":null,"pages":null},"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":null,"pages":null},"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 : 2024-04-25DOI: 10.1088/1361-6420/ad438c
Heping Dong, Peijun Li
This paper addresses an inverse cavity scattering problem associated with the time-harmonic biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the solution to the boundary value problem, and the one-to-one correspondence is confirmed between the Helmholtz component of biharmonic waves and the resulting far-field patterns. Two mixed reciprocity relations are deduced, linking the scattered field generated by plane waves to the far-field pattern produced by various types of point sources. Furthermore, the symmetry relations are explored for the scattered fields generated by point sources. Finally, we present two uniqueness results for the inverse problem by utilizing both far-field patterns and phaseless near-field data.
{"title":"Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation","authors":"Heping Dong, Peijun Li","doi":"10.1088/1361-6420/ad438c","DOIUrl":"https://doi.org/10.1088/1361-6420/ad438c","url":null,"abstract":"\u0000 This paper addresses an inverse cavity scattering problem associated with the time-harmonic biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the solution to the boundary value problem, and the one-to-one correspondence is confirmed between the Helmholtz component of biharmonic waves and the resulting far-field patterns. Two mixed reciprocity relations are deduced, linking the scattered field generated by plane waves to the far-field pattern produced by various types of point sources. Furthermore, the symmetry relations are explored for the scattered fields generated by point sources. Finally, we present two uniqueness results for the inverse problem by utilizing both far-field patterns and phaseless near-field data.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140657922","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 : 2024-04-24DOI: 10.1088/1361-6420/ad42cd
Seongyeon Kim, Sunghwan Moon, Ihyeok Seo
In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is based on generating acoustic waves inside of an object of interest and one of the mathematical problem in PAT is reconstructing the initial velocity from the solution of the wave equation measured on the outside of object. Using the spherical harmonics and spectral theorem, we demonstrate a way to recover the initial velocity.
{"title":"Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations","authors":"Seongyeon Kim, Sunghwan Moon, Ihyeok Seo","doi":"10.1088/1361-6420/ad42cd","DOIUrl":"https://doi.org/10.1088/1361-6420/ad42cd","url":null,"abstract":"\u0000 In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is based on generating acoustic waves inside of an object of interest and one of the mathematical problem in PAT is reconstructing the initial velocity from the solution of the wave equation measured on the outside of object. Using the spherical harmonics and spectral theorem, we demonstrate a way to recover the initial velocity.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140665432","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":null,"pages":null},"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}
Pub Date : 2024-04-22DOI: 10.1088/1361-6420/ad4171
Hao-Jie Hu, Jiawen Li, Li-Ye Xiao, Yu Cheng, Qing Huo Liu
Many successful machine learning methods have been developed for electromagnetic inverse scattering problems. However, so far, their inversion has been performed only at the specifically trained frequencies. To make the machine learning based inversion method more generalizable for realistic engineering applications, this work proposes a residual fully convolutional network (Res-FCN) to perform EM inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band. The proposed Res-FCN combines the advantages of the Res-Net and the fully convolutional network (FCN). Res-FCN consists of an encoder and a decoder: the encoder is employed to extract high-dimensional features from the measured scattered field through the residual frameworks, while the decoder is employed to map from the high-dimensional features extracted by the encoder to the electrical parameter distribution in the inversion region by the up-sample layer and the residual frameworks. Four numerical examples verify that the proposed Res-FCN can achieve good performance in the 2-D EM inversion problem for high contrast scatterers with anti-noise ability at an arbitrary frequency point within a wide frequency band.
{"title":"A residual fully convolutional network (Res-FCN) for electromagnetic inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band","authors":"Hao-Jie Hu, Jiawen Li, Li-Ye Xiao, Yu Cheng, Qing Huo Liu","doi":"10.1088/1361-6420/ad4171","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4171","url":null,"abstract":"\u0000 Many successful machine learning methods have been developed for electromagnetic inverse scattering problems. However, so far, their inversion has been performed only at the specifically trained frequencies. To make the machine learning based inversion method more generalizable for realistic engineering applications, this work proposes a residual fully convolutional network (Res-FCN) to perform EM inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band. The proposed Res-FCN combines the advantages of the Res-Net and the fully convolutional network (FCN). Res-FCN consists of an encoder and a decoder: the encoder is employed to extract high-dimensional features from the measured scattered field through the residual frameworks, while the decoder is employed to map from the high-dimensional features extracted by the encoder to the electrical parameter distribution in the inversion region by the up-sample layer and the residual frameworks. Four numerical examples verify that the proposed Res-FCN can achieve good performance in the 2-D EM inversion problem for high contrast scatterers with anti-noise ability at an arbitrary frequency point within a wide frequency band.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674359","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 : 2024-04-19DOI: 10.1088/1361-6420/ad40c9
Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou
In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-$p$ (t-log-$S_p$) low-rank measure and a tensor iteratively reweighted Schatten-$p$ minimization (t-IRSpM) algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-$p$ minimization (TLSpM) method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.
{"title":"3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization","authors":"Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou","doi":"10.1088/1361-6420/ad40c9","DOIUrl":"https://doi.org/10.1088/1361-6420/ad40c9","url":null,"abstract":"\u0000 In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-$p$ (t-log-$S_p$) low-rank measure and a tensor iteratively reweighted Schatten-$p$ minimization (t-IRSpM) algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-$p$ minimization (TLSpM) method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140684994","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}
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