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Undersampled Magnetic Resonance Image Reconstructions Based on a Combination of U-Nets and L1, L2, and TV Optimizations

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Undersampled Magnetic Resonance Image Reconstructions Based ...

IEEE International Workshop on Imaging Systems and Techniques (IST)

作者： Aline A.S. Thomaz Jonathan A.S. Lima Cristiano J. Miosso Mylé ne C.Q. Farias Andrey S. Krylov Yong Ding Department of Electrical Engineering University of Brasilia (UnB) Brasilia Brazil Biomedical Engineering Graduate Program University of Brasilia (UnB) Brasilia Brazil Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russia College of Information Science and Electronic Engineering Zhejiang University Zhejiang China

Magnetic Resonance Imaging (MRI) plays a major role in the diagnosis of several diseases. However, the acquisition of measurements in the k-space domain, which is the basis for image reconstruction, takes a long time compared to other imaging modalities and is comparatively costly. In this context, undersampled MRI reconstruction is an approach for decreasing the acquisition duration and the exam's final cost. With this objective, both Compressed Sensing (CS) and Deep Learning (DL) provide techniques for generating good quality MRI images from undersampled measurements. In this paper, we combine CS and DL methods in order to investigate the potential increase in image quality over each isolated approach. We use reconstructions from from highly undersampled MRI signals using two CS approaches, the L1 and total minimizations, as inputs to a U-Net. We also use, for comparison, the reconstructions from the same undersampled signals using L2 minimization, and also test them as inputs to a U-net. The goal is to evaluate whether the the U-Net can improve the results of the CS reconstructions after learning from degraded and original image pairs. Our experimental results suggest that the combination of L1 or TV minimization with U-Nets can improve reconstruction, in terms of objective image quality, over each technique used in isolation.

关键词： Image quality TV Magnetic resonance imaging Magnetic resonance Minimization Time measurement Sensors

Biwhitening reveals the rank of a count matrix

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arXiv 2021年

作者： Landa, Boris Zhang, Thomas T.C.K. Kluger, Yuval Program in Applied Mathematics Yale University United States Department of Electrical and Systems Engineering University of Pennsylvania United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University United States Department of Pathology Yale University School of Medicine United States

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we consider a Poisson random matrix with independent entries, and propose a simple procedure termed biwhitening for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one can scale the rows and columns of the data matrix simultaneously so that the spectrum of the corresponding noise agrees with the standard Marchenko-Pastur (MP) law, justifying the use of the MP upper edge as a threshold for rank selection. Importantly, the required scaling factors can be estimated directly from the observations by solving a matrix scaling problem via the Sinkhorn-Knopp algorithm. Aside from the Poisson, our approach is extended to families of distributions that satisfy a quadratic relation between the mean and the variance, such as the generalized Poisson, binomial, negative binomial, gamma, and many others. This quadratic relation can also account for missing entries in the data. We conduct numerical experiments that corroborate our theoretical findings, and showcase the advantage of our approach for rank estimation in challenging regimes. Furthermore, we demonstrate the favorable performance of our approach on several real datasets of single-cell RNA sequencing (scRNA-seq), High-Throughput Chromosome Conformation Capture (Hi-C), and document topic *** Codes 62H12, 62H25. Copyright © 2021, The Authors. All rights reserved.

关键词： Random variables

Measuring 3D Chemistry at 1 nm Resolution with Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1394-1395页

作者： Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Cho, Min Gee Qian, Yiwen Gu, Junsi Rozeveld, Steve Ercius, Peter Fessler, Jeffrey A. Xu, Ting Scott, Mary Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Advanced Photon Source Argonne National Laboratory Lemont IL United States Department of Materials Science and Engineering University of California at Berkeley Berkeley CA United States National Center for Electron Microscopy Lawrence Berkeley National Laboratory Berkeley CA United States Dow Chemical Co. Midland MI United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Materials Science Division Lawrence Berkeley National Laboratory Berkeley CA United States Applied Physics Program University of Michigan Ann Arbor MI United States

Vortex shedding and heat transfer from a heated circular cylinder in Bingham plastic fluids

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arXiv 2024年

作者： Peng, Sai Li, Xiang Yu, Li Zhuang, Xiaoru Yu, Peng School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen518055 China National Center for Applied Mathematics in Hunan Xiangtan411105 China School of Civil Engineering and Architecture Southwest University of Science and Technology Mianyang621010 China Center for Complex Flows and Soft Matter Research Southern University of Science and Technology Shenzhen518055 China School of Mechanical and Electrical Engineering Shenzhen Polytechnic University Shenzhen518055 China

The present study numerically investigates the vortex shedding and heat transfer characteristics of a heated circular cylinder immersed in Bingham plastic fluids. The effects of three parameters, i.e., (i) plastic Reynolds number (10 ≤ Re ≤ 180), (ii) Prandtl number (1 ≤ Pr ≤ 100), and (iii) the Bingham number (0 ≤ Bn ≤ 104), are evaluated. The Navier-Stokes and energy equations for flow and heat transfer are adopted, along with the incorporation of the Papanastasiou regularization to address the discontinuous-viscosity characteristics of Bingham plastic fluids. To illustrate the impact of fluid yield stress on the flow structure, the study provides comprehensive insights into flow transition, streamlines, shear rate and velocity distributions, the morphology of yielded/unyielded regions, and the drag coefficient (Cd). Additionally, the temperature distribution, the local Nusselt number (Nu ̅local ) along the cylinder, and the average Nusselt number on the cylinder (Nu ̅ ) are analyzed. The results indicate that the flow transition of Bingham fluids over a circular cylinder is dependent on external disturbances, exhibiting subcritical bifurcation behavior. This leads to abrupt jumps in the C̅d - Bn curve and the Nu ̅ - Bn curve near the critical Bingham number Bnc. Furthermore, the heat transfer performance is contingent upon the different distribution of shear strain rate in the boundary layer across various Bn ranges. It is observed that Nu ̅ and Bn fits well with the Carreau-Yasuda-like non-Newtonian viscosity model. This investigation enhances the understanding of the vortex shedding and heat transfer behaviors in Bingham plastic fluids. © 2024, CC BY.

关键词： Vortex shedding

Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the 2s − 3s or 2s − 4s transition in hydrogen

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arXiv 2023年

作者： Li, Jiguang Derevianko, Andrei Elliott, D.S. Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Physics University of Nevada RenoNV89557 United States Department of Physics and Astronomy Purdue University West LafayetteIN47907 United States School of Electrical and Computer Engineering Purdue University West LafayetteIN47907 United States Purdue Quantum Science and Engineering Institute Purdue University West LafayetteIN47907 United States

We explore the feasibility of extracting electroweak observables from a measurement of atomic parity violation in hydrogen. Our proposed quantum-control scheme focuses on the 2s−3s or 2s−4s transitions in hydrogen. This work is motivated by the recently observed anomaly in the W-boson mass, which may substantially modify the Standard Model value of the proton weak charge. We also study the accuracy of the previously employed approximations in computing parity-violating effects in hydrogen. © 2023, CC BY.

关键词： Hydrogen

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems: publisher’s note

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Optics Letters 2025年第10期50卷 3356-3356页

作者： Nikolaos K. Efremidis Demetrios N. Christodoulides Department of Applied Mathematics University of Crete Heraklion 71409 Greece Institute of Applied and Computational Mathematics FORTH Heraklion Crete 70013 Greece Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles California 90089 USA

This publisher’s note contains a correction to Opt. Lett. 49 , 2777 (2024 [ CrossRef ] ).

关键词： Composite materials Optical systems

Unbiased Estimation Using a Class of Diffusion Processes

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SSRN

SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

The Role of Heterogeneity in Autonomous Perimeter Defense Problems

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arXiv 2022年

作者： Adler, Aviv Mickelin, Oscar Ramachandran, K. Sukhatme, Gaurav S. Karaman, Sertac Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamic programming

Deep potentials for materials science

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材料展望（英文）

材料展望（英文） 2022年第2期 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople's Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople's Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China International Digital Economy Academy(IDEA) ShenzhenPeople's Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network