Inverse Problems最新文献_第6页

A direct sampling method for time-fractional diffusion equation 时间分数扩散方程的直接采样法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-18 DOI: 10.1088/1361-6420/ad4051

Lingyun Qiu, Jiwoon Sim

引用次数: 0

Cone-beam consistency conditions for planar trajectories with parallel and perpendicular detectors 带有平行和垂直探测器的平面轨迹的锥形光束一致性条件

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-17 DOI: 10.1088/1361-6420/ad3fe3

Hung Nguyen, R. Clackdoyle, L. Desbat

{"title":"Cone-beam consistency conditions for planar trajectories with parallel and perpendicular detectors","authors":"Hung Nguyen, R. Clackdoyle, L. Desbat","doi":"10.1088/1361-6420/ad3fe3","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3fe3","url":null,"abstract":"\u0000 Cone-beam (CB) projections provide a first-order model for x-ray imaging with an area detector. CB consistency conditions (CBCCs), also known as range conditions for the 3D divergent x-ray transform, are equations that express the redundant information in a collection of CB projections. For applications purposes, CBCCs are most suitably expressed in terms of detector coordinates. CBCCs are only known for a few geometrical configurations, which depend on the source and detector trajectories. Here we only consider source trajectories that lie in a plane, and detector orientations that are parallel to the trajectory plane, or perpendicular to it. The parallel detector is stationary, but the vertical detector rotates around the center of the circular trajectory. We unify and generalize the existing known CBCCs for planar trajectories, by creating an intermediate geometry consisting of a parallel, rotating detector, and we develop new CBCCs for this geometry. Our main result is a theorem on CBCCs for a perpendicular detector, which must necessarily move in response to movement of the source. We also provide a theorem for the more difficult situation of a perpendicular detector but without the restriction that the target object be on one side or the other of the trajectory plane. We present a simple numerical simulations for a toy calibration problem to provide an example application of the new CBCCs.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140692309","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":null,"pages":null},"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

Bayesian model error method for the passive inverse scattering problem 被动反向散射问题的贝叶斯模型误差法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-16 DOI: 10.1088/1361-6420/ad3f40

Yunwen Yin, Liang Yan

引用次数: 0

Application of a mild data-driven technique to Lippmann-Schwinger inverse scattering in variable-exponent Lebesgue spaces for microwave imaging 将温和的数据驱动技术应用于微波成像可变分量勒贝格空间中的李普曼-施温格反散射技术

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-15 DOI: 10.1088/1361-6420/ad3ea9

C. Estatico, V. Schenone, A. Fedeli, Andrea Randazzo

引用次数: 0

Contrast source inversion of sparse targets through multi-resolution Bayesian compressive sensing 通过多分辨率贝叶斯压缩传感对稀疏目标进行对比源反演

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-04-05 DOI: 10.1088/1361-6420/ad3b33

M. Salucci, L. Poli, F. Zardi, L. Tosi, Samantha Lusa, A. Massa

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":null,"pages":null},"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":null,"pages":null},"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