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DOTnet 2.0: Deep learning network for diffuse optical tomography image reconstruction

Intelligence-Based Medicine 2024年 9卷 100133-100133页

作者： Ko, Zhen Yu Gordon Li, Yang Liu, Jiulong Ji, Hui Qiu, Anqi Chen, Nanguang Department of Biomedical Engineering National University of Singapore Singapore Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing China Department of Mathematics National University of Singapore Singapore Department of Biomedical Engineering Johns Hopkins University Baltimore MD United States Department of Health Technology and Informatics The Hong Kong Polytechnic University (PolyU) Hong Kong Hong Kong National University of Singapore (Suzhou) Research Institute Suzhou Industrial Park Jiangsu Suzhou China

Breast cancer is the most common cancer worldwide. The standard imaging modality for breast cancer screening is X-ray mammography, which suffers from low sensitivities in women with dense breasts and can potentially cause cancers despite a low radiation dosage. Diffuse Optical Tomography (DOT) is a noninvasive imaging technique that can potentially be employed to improve breast cancer early detection. However, conventional model-based algorithms for reconstructing DOT images usually produce low-quality images with limited resolution and low reconstruction accuracy. We propose to integrate deep neural networks (DNNs) with the conventional DOT reconstruction methods. This hybrid framework significantly enhances image quality. The DNNs have been trained and tested with sample data derived from clinically relevant breast models. The sample dataset contains blood vessel structures from breast structures and artificially created vessels using the Lindenmayer-system algorithm. By comparing the hybrid reconstruction with the ground truth image, we demonstrated a multi scale - structural similarity index measure (MS-SSIM) score of 0.80–0.90. Whereas using conventional reconstruction, MS-SSIM provided a much inferior score of 0.36–0.59. In terms of DOT image quality, both qualitative and quantitative assessments of the reconstructed images signify that the hybrid approach is superior to conventional methods. This improvement suggests that DOT can potentially become a viable alternative to breast cancer screening, providing a step towards the next-generation device for optical mammography. © 2024 The Authors

关键词： Breast cancer Convolutional neural network Deep learning Diffuse optical tomography Image reconstruction

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Machine Learning-based Signal Quality Assessment for Cardiac Volume Monitoring in Electrical Impedance Tomography

arXiv

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arXiv 2023年

作者： Hyun, Chang Min Jang, Tae Jun Nam, Jeongchan Kwon, Hyeuknam Jeon, Kiwan Lee, Kyunghun School of Mathematics and Computing Computational Science and Engineering Yonsei University Seoul Korea Republic of BiLab Pangyo Korea Republic of Division of Software Yonsei University Wonju Korea Republic of National Institute for Mathematical Sciences Daejeon Korea Republic of Kyung Hee University Seoul Korea Republic of

Owing to recent advances in thoracic electrical impedance tomography, a patient's hemodynamic function can be noninvasively and continuously estimated in real-time by surveilling a cardiac volume signal associated with stroke volume and cardiac output. In clinical applications, however, a cardiac volume signal is often of low quality, mainly because of the patient's deliberate movements or inevitable motions during clinical interventions. This study aims to develop a signal quality indexing method that assesses the influence of motion artifacts on transient cardiac volume signals. The assessment is performed on each cardiac cycle to take advantage of the periodicity and regularity in cardiac volume changes. Time intervals are identified using the synchronized electrocardiography system. We apply divergent machine-learning methods, which can be sorted into discriminative-model and manifold-learning approaches. The use of machine-learning could be suitable for our real-time monitoring application that requires fast inference and automation as well as high accuracy. In the clinical environment, the proposed method can be utilized to provide immediate warnings so that clinicians can minimize confusion regarding patients' conditions, reduce clinical resource utilization, and improve the confidence level of the monitoring system. Numerous experiments using actual EIT data validate the capability of cardiac volume signals degraded by motion artifacts to be accurately and automatically assessed in real-time by machine learning. The best model achieved an accuracy of 0.95, positive and negative predictive values of 0.96 and 0.86, sensitivity of 0.98, specificity of 0.77, and AUC of 0.96. © 2023, CC BY.

关键词： Machine learning

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A Greedy Sensor Selection Algorithm for Hyperparameterized Linear Bayesian Inverse Problems

arXiv

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arXiv 2023年

作者： Aretz, Nicole Chen, Peng Degen, Denise D. Veroy, Karen Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th St AustinTX78712 United States School of Computational Science and Engineering Georgia Institute of Technology 756 W Peachtree St NW AtlantaGA30308 United States Computational Geoscience Geothermics and Reservoir Geophysics RWTH Aachen University Mathieustr. 30 Aachen52074 Germany Center for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven5612 AZ Netherlands

We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed physical system. To optimally reduce the uncertainty in the system’s model with a single set of sensors, the initial sensor placement needs to account for the non-linear state changes of all admissible configurations. We address this requirement through an observability coefficient which links the posteriors’ uncertainties directly to the choice of sensors. We propose a greedy sensor selection algorithm to iteratively improve the observability coefficient for all configurations through orthogonal matching pursuit. The algorithm allows explicitly correlated noise models even for large sets of candidate sensors, and remains computationally efficient for high-dimensional forward models through model order reduction. We demonstrate our approach on a large-scale geophysical model of the Perth Basin, and provide numerical studies regarding optimality and scalability with regard to classic optimal experimental design utility functions. © 2023, CC BY.

关键词： Inverse problems

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Students' Development of a Logarithm Function in Python Using Taylor Expansions: a Teaching Design Case Study

引用

Digital experiences in mathematics education 2022年第2期8卷 213-255页

作者： Odd Petter Sand Elise Lockwood Marcos D Caballero Knut Mørken Centre for Computing in Science Education (CCSE) University of Oslo N-0316 Oslo Norway. Department of Mathematics Oregon State University Corvallis OR 97331 USA. Department of Physics and Astronomy Department of Computational Mathematics Science and Engineering and CREATE for STEM Institute Michigan State University East Lansing MI 48823 USA.

We present here the lessons learned by iteratively designing a tutorial for first-year university students using computer programming to work with mathematical models. Alternating between design and implementation, we used video-taped task interviews and classroom observations to ensure that the design promoted student understanding. The final version of the tutorial we present here has students make their own logarithm function from scratch, using Taylor polynomials. To ensure that the resulting function is accurate and reasonably fast, the students had to understand and apply concepts both from computing and from mathematics. We identify three categories of such concepts and identify three design features that students attended to when demonstrating such understanding. Additionally, we describe four important take-aways from a teaching design point of view that resulted from this iterative design process.

关键词： Backward design computing mathematics Taylor polynomials Understanding

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Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

SSRN

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SSRN 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel's principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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Quantum Circuits for the heat equation with physical boundary conditions via Schrödingerisation

arXiv

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arXiv 2024年

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

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Automatic 3D Registration of Dental CBCT and Face Scan Data using 2D Projection Images

arXiv

引用

arXiv 2023年

作者： Park, Hyoung Suk Hyun, Chang Min Lee, Sang-Hwy Seo, Jin Keun Jeon, Kiwan National Institute for Mathematical Sciences Daejeon34047 Korea Republic of School of Mathematics and Computing Computational Science and Engineering Yonsei University Seoul03722 Korea Republic of Department of Oral and Maxillofacial Surgery Oral Science Research Center College of Dentistry Yonsei University Seoul03722 Korea Republic of

This paper presents a fully automatic registration method of dental cone-beam computed tomography (CBCT) and face scan data. It can be used for a digital platform of 3D jaw-teeth-face models in a variety of applications, including 3D digital treatment planning and orthognathic surgery. Difficulties in accurately merging facial scans and CBCT images are due to the different image acquisition methods and limited area of correspondence between the two facial surfaces. In addition, it is difficult to use machine learning techniques because they use face-related 3D medical data with radiation exposure, which are difficult to obtain for training. The proposed method addresses these problems by reusing an existing machine-learning-based 2D landmark detection algorithm in an open-source library and developing a novel mathematical algorithm that identifies paired 3D landmarks from knowledge of the corresponding 2D landmarks. A main contribution of this study is that the proposed method does not require annotated training data of facial landmarks because it uses a pre-trained facial landmark detection algorithm that is known to be robust and generalized to various 2D face image models. Note that this reduces a 3D landmark detection problem to a 2D problem of identifying the corresponding landmarks on two 2D projection images generated from two different projection angles. Here, the 3D landmarks for registration were selected from the sub-surfaces with the least geometric change under the CBCT and face scan environments. For the final fine-tuning of the registration, the Iterative Closest Point method was applied, which utilizes geometrical information around the 3D landmarks. The experimental results show that the proposed method achieved an averaged surface distance error of 0.74 mm for three pairs of CBCT and face scan *** Codes 92C55, 15A04, 62F10 © 2023, CC BY.

关键词： Iterative methods

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Adversarially robust clustering with optimality guarantees

arXiv

引用

arXiv 2023年

作者： Jana, Soham Yang, Kun Kulkarni, Sanjeev The Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States The Data Science Institute Center For Research Computing Southern Methodist University DallasTX United States The Department of Operations Research and Financial Engineering Princeton University PrincetonNJ United States

We consider the problem of clustering data points coming from sub-Gaussian mixtures. Existing methods that provably achieve the optimal mislabeling error, such as the Lloyd algorithm, are usually vulnerable to outliers. In contrast, clustering methods seemingly robust to adversarial perturbations are not known to satisfy the optimal statistical guarantees. We propose a simple robust algorithm based on the coordinatewise median that obtains the optimal mislabeling rate even when we allow adversarial outliers to be present. Our algorithm achieves the optimal error rate in constant iterations when a weak initialization condition is satisfied. In the absence of outliers, in fixed dimensions, our theoretical guarantees are similar to that of the Lloyd algorithm. Extensive experiments on various simulated and public datasets are conducted to support the theoretical guarantees of our *** Codes 62G30, 62G35, 62H30 Copyright © 2023, The Authors. All rights reserved.

关键词： Clustering algorithms

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Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions

arXiv

引用

arXiv 2022年

作者： Hou, Pengyu Liu, Fang Zhou, Aihui School of Mathematical Sciences Beijing Normal University Beijing100875 China School of Statistics and Mathematics Central University of Finance and Economics Beijing102206 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to the finite element approximations on a much coarse grid and a univariant fine grid. It is shown by both theory and numerics including electronic structure calculations that the resulting approximation still maintains an asymptotically optimal accuracy. Consequently the symmetrized two-scale finite element method reduces computational cost *** Codes 65N15, 65N25, 65N30, 65N50 Copyright © 2022, The Authors. All rights reserved.

关键词： Partial differential equations

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Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

arXiv

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arXiv 2023年

作者： Zanoni, Andrea Geraci, Gianluca Salvador, Matteo Menon, Karthik Marsden, Alison L. Schiavazzi, Daniele E. Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Pediatric Cardiology Stanford University StanfordCA United States Bioengineering Stanford University StanfordCA United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches. Copyright © 2023, The Authors. All rights reserved.

关键词： Probability distributions

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