Inverse Problems最新文献_第6页

A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution 用于多光子显微镜图像复原的新型变分法：从 PSF 估计到 3D 解卷积

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-23 DOI: 10.1088/1361-6420/ad3c67

Julien Ajdenbaum, Emilie Chouzenoux, Claire Lefort, Ségolène Martin and Jean-Christophe Pesquet

{"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}

引用次数: 0

Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data 部分数据一阶扰动双谐算子反边界值问题的稳定性估计

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-17 DOI: 10.1088/1361-6420/ad3be6

Boya Liu

引用次数: 0

L2SR: learning to sample and reconstruct for accelerated MRI via reinforcement learning L2SR：通过强化学习为加速核磁共振成像学会采样和重建

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-17 DOI: 10.1088/1361-6420/ad3b34

Pu Yang and Bin Dong

{"title":"L2SR: learning to sample and reconstruct for accelerated MRI via reinforcement learning","authors":"Pu Yang and Bin Dong","doi":"10.1088/1361-6420/ad3b34","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3b34","url":null,"abstract":"Magnetic resonance imaging (MRI) is a widely used medical imaging technique, but its long acquisition time can be a limiting factor in clinical settings. To address this issue, researchers have been exploring ways to reduce the acquisition time while maintaining the reconstruction quality. Previous works have focused on finding either sparse samplers with a fixed reconstructor or finding reconstructors with a fixed sampler. However, these approaches do not fully utilize the potential of joint learning of samplers and reconstructors. In this paper, we propose an alternating training framework for jointly learning a good pair of samplers and reconstructors via deep reinforcement learning. In particular, we consider the process of MRI sampling as a sampling trajectory controlled by a sampler, and introduce a novel sparse-reward partially observed Markov decision process (POMDP) to formulate the MRI sampling trajectory. Compared to the dense-reward POMDP used in existing works, the proposed sparse-reward POMDP is more computationally efficient and has a provable advantage. Moreover, the proposed framework, called learning to sample and reconstruct (L2SR), overcomes the training mismatch problem that arises in previous methods that use dense-reward POMDP. By alternately updating samplers and reconstructors, L2SR learns a pair of samplers and reconstructors that achieve state-of-the-art reconstruction performances on the fastMRI dataset. Codes are available at https://github.com/yangpuPKU/L2SR-Learning-to-Sample-and-Reconstruct.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806620","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}

引用次数: 0

Deep unrolling networks with recurrent momentum acceleration for nonlinear inverse problems 针对非线性逆问题的具有递归动量加速功能的深度开卷网络

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-02 DOI: 10.1088/1361-6420/ad35e3

Qingping Zhou, Jiayu Qian, Junqi Tang, Jinglai Li

{"title":"Deep unrolling networks with recurrent momentum acceleration for nonlinear inverse problems","authors":"Qingping Zhou, Jiayu Qian, Junqi Tang, Jinglai Li","doi":"10.1088/1361-6420/ad35e3","DOIUrl":"https://doi.org/10.1088/1361-6420/ad35e3","url":null,"abstract":"Combining the strengths of model-based iterative algorithms and data-driven deep learning solutions, deep unrolling networks (DuNets) have become a popular tool to solve inverse imaging problems. Although DuNets have been successfully applied to many linear inverse problems, their performance tends to be impaired by nonlinear problems. Inspired by momentum acceleration techniques that are often used in optimization algorithms, we propose a recurrent momentum acceleration (RMA) framework that uses a long short-term memory recurrent neural network (LSTM-RNN) to simulate the momentum acceleration process. The RMA module leverages the ability of the LSTM-RNN to learn and retain knowledge from the previous gradients. We apply RMA to two popular DuNets—the learned proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods, resulting in LPGD-RMA and LPD-RMA, respectively. We provide experimental results on two nonlinear inverse problems: a nonlinear deconvolution problem, and an electrical impedance tomography problem with limited boundary measurements. In the first experiment we have observed that the improvement due to RMA largely increases with respect to the nonlinearity of the problem. The results of the second example further demonstrate that the RMA schemes can significantly improve the performance of DuNets in strongly ill-posed problems.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"240 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561607","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}

引用次数: 0

Convergence of non-linear diagonal frame filtering for regularizing inverse problems 用于正则化逆问题的非线性对角框滤波的收敛性

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-26 DOI: 10.1088/1361-6420/ad3333

Andrea Ebner, Markus Haltmeier

{"title":"Convergence of non-linear diagonal frame filtering for regularizing inverse problems","authors":"Andrea Ebner, Markus Haltmeier","doi":"10.1088/1361-6420/ad3333","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3333","url":null,"abstract":"Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization techniques have been proposed. In particular, the use of filtered diagonal frame decompositions (DFDs) has proven to be effective and computationally efficient. However, existing convergence analysis applies only to linear filters and a few non-linear filters such as soft thresholding. In this paper, we analyze filtered DFDs with general non-linear filters. In particular, our results generalize singular value decomposition-based spectral filtering from linear to non-linear filters as a special case. As a first approach, we establish a connection between non-linear diagonal frame filtering and variational regularization, allowing us to use results from variational regularization to derive the convergence of non-linear spectral filtering. In the second approach, as our main theoretical results, we relax the assumptions involved in the variational case while still deriving convergence. Furthermore, we discuss connections between non-linear filtering and plug-and-play regularization and explore potential benefits of this relationship.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315439","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}

引用次数: 0

Inverse spectral problem for the Schrödinger operator on the square lattice 方格上薛定谔算子的逆谱问题

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-25 DOI: 10.1088/1361-6420/ad3332

Dongjie Wu, Chuan-Fu Yang, Natalia Pavlovna Bondarenko

引用次数: 0

Towards optimal sensor placement for inverse problems in spaces of measures 在度量空间中实现逆问题的最佳传感器布局

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-25 DOI: 10.1088/1361-6420/ad2cf8

Phuoc-Truong Huynh, Konstantin Pieper, Daniel Walter

{"title":"Towards optimal sensor placement for inverse problems in spaces of measures","authors":"Phuoc-Truong Huynh, Konstantin Pieper, Daniel Walter","doi":"10.1088/1361-6420/ad2cf8","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2cf8","url":null,"abstract":"The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316622","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}

引用次数: 0

A stochastic ADMM algorithm for large-scale ptychography with weighted difference of anisotropic and isotropic total variation 利用各向异性和各向同性总变化的加权差值进行大规模分层成像的随机 ADMM 算法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-20 DOI: 10.1088/1361-6420/ad2cfa

Kevin Bui, Zichao (Wendy) Di

引用次数: 0

Stable determination of an impedance obstacle by a single far-field measurement 通过单次远场测量稳定确定阻抗障碍物

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-19 DOI: 10.1088/1361-6420/ad3087

Huaian Diao, Hongyu Liu, Longyue Tao

{"title":"Stable determination of an impedance obstacle by a single far-field measurement","authors":"Huaian Diao, Hongyu Liu, Longyue Tao","doi":"10.1088/1361-6420/ad3087","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3087","url":null,"abstract":"We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in <inline-formula>\u0000<tex-math><?CDATA $mathbb{R}^2$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ipad3087ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. The obstacle is the polygonal shape and the surface impedance parameter is non-zero constant. We establish the stability results using a single far-field pattern, constituting a longstanding problem in the inverse scattering theory. This is the first stability result in the literature in determining an impedance obstacle by a single far-field measurement. The stability in simultaneously determining the obstacle and the boundary impedance is established in terms of the classical Hausdorff distance. Several technical novelties and developments in the mathematical strategy developed for establishing the aforementioned stability results exist. First, the stability analysis is conducted around a corner point in a micro-local manner. Second, our stability estimates establish explicit relationships between the obstacle’s geometric configurations and the wave field’s vanishing order at the corner point. Third, we develop novel error propagation techniques to tackle singularities of the wave field at a corner with the impedance boundary condition.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315443","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}

引用次数: 0

A single level set function approach for multiple material-phases applied to full-waveform inversion in the time domain 应用于时域全波形反演的多材料相单一水平集函数方法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-03-19 DOI: 10.1088/1361-6420/ad2eca

P B de Castro, E C N Silva, E A Fancello

引用次数: 0