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Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

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arXiv 2020年

作者： Chen, Yunmei Liu, Hongcheng Ye, Xiaojing Zhang, Qingchao Department of Mathematics University of Florida GainesvilleFL32611 United States Industrial and Systems Engineering University of Florida GainesvilleFL32611 United States Department of Mathematics and Statistics Georgia State University AtlantaGA30303 United States

We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the l2,1 norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the convergence properties of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice. Copyright © 2020, The Authors. All rights reserved.

关键词： Image reconstruction

Enabling Research through the SCIP Optimization Suite 8.0

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arXiv 2023年

作者： Bestuzheva, Ksenia Besançon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher van der Hulst, Rolf Koch, Thorsten Lübbecke, Marco Maher, Stephen J. Matter, Frederic Mühmer, Erik Müller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schlösser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany ZIB-AIS2T Germany School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Eindhoven University of Technology Department of Mathematics and Computer Science Netherlands ZIB-AIS2T I2DAMO GmbH Englerallee 19 Berlin14195 Germany ZIB-AIS2T HTW Berlin Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany ZIB Department A2IM Takustr. 7 Berlin14195 Germany RWTH Aachen-Lehrstuhl für OR Germany University of Exeter College of Engineering Mathematics and Physical Sciences Exeter United Kingdom Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany TU Darmstadt Fachbereich Mathematik Germany ZIB-A2IM Germany TU Berlin Germany ZIB-A2IM Software and Algorithms for Discrete Optimization Institute of Mathematics TU Berlin Germany GAMS Software GmbH c/o ZIB-AIS2T Germany

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this paper is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon *** Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05 Copyright © 2023, The Authors. All rights reserved.

关键词： Integer programming

Linearization of two-state thruster models 5

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Linearization of two-state thruster models

5th International Conference on mathematics: Pure, Applied and Computation, ICoMPAC 2019

作者： Adzkiya, Dieky Nurhadi, Hendro Herlambang, Teguh Department of Mathematics Institut Teknologi Sepuluh Nopember Indonesia Department of Industrial Mechanical Engineering Institut Teknologi Sepuluh Nopember Indonesia Center of Excellence for Mechatronics and Industrial Automation Research Center Institut Teknologi Sepuluh Nopember Indonesia Study Program of Information Systems Universitas Nahdlatul Ulama Surabaya Indonesia

A thruster is a device used for station keeping, attitude control, in the reaction control system, or long-duration, low-thrust acceleration. Thruster is one of the main components in autonomous surface vehicle. In this paper, we discuss the linearization of two-state thruster model by using the Jacobian method. © Published under licence by IOP Publishing Ltd.

关键词： Linearization

Image Recovery from Rotational And Translational Invariants

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Image Recovery from Rotational And Translational Invariants

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix and Applications in Multi-Source Network Coding

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arXiv 2022年

作者： Liu, Hedongliang Wei, Hengjia Wachter-Zeh, Antonia Schwartz, Moshe The School of Computation Information and Technology Technical University of Munich Munich80333 Germany The Peng Cheng Laboratory Shenzhen518055 China School of Mathematics and Statistics Xi’an Jiaotong University Xi’an710049 China Guangzhou510555 China The School of Electrical and Computer Engineering Ben-Gurion University of the Negev Beer Sheva8410501 Israel The Department of Electrical and Computer Engineering McMaster University HamiltonONL8S 4K1 Canada

Linearized Reed-Solomon (LRS) codes are evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary and sufficient conditions for the existence of MSRD codes with a support-constrained generator matrix. The conditions on the support constraints are identical to those for MDS codes and MRD codes. The required field size for an rn, ksqm LRS codes with support-constrained generator matrix is q ě ` 1 and m ě maxlPrstk ´ 1 ` logq k, nlu, where is the number of blocks and nl is the size of the l-th block. The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes. For the support constraints that do not satisfy the necessary conditions, we derive the maximum sum-rank distance of a code whose generator matrix fulfills the constraints. Such a code can be constructed from a subcode of an LRS code with a sufficiently large field size. Moreover, as an application in network coding, the conditions can be used as constraints in an integer programming problem to design distributed LRS codes for a distributed multi-source network. Copyright © 2022, The Authors. All rights reserved.

关键词： Reed-Solomon codes

Optical wave solutions of perturbed time-fractional nonlinear Schrödinger equation

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Journal of Ocean engineering and Science 2022年

作者： Wang, Fuzhang Salama, Samir A. Khater, Mostafa M.A. School of Mathematical and Statistics Xuzhou University of Technology Jiangsu Xuzhou 221018 China Nanchang Institute of Technology Nanchang 330044 China Division of Biochemistry Department of Pharmacology College of Pharmacy Taif University Taif P.O. Box 11099 Saudi Arabia Department of Mathematics Faculty of Science Jiangsu University 212013 China Department of Basic Science Obour High Institute for Engineering and Technology Cairo 11828 Egypt

The conformable fractional derivatives modified Khater (mKhat.) technique and the Adomian decomposition (AD) method is used to examine the perturbed time-fractional nonlinear Schrödinger (NLS) problem's analytical and semi-analytical wave solutions. This model describes the dynamics of optical solitons propagating via nonlinear optical fibers. For this model, we create a variety of different formulae for analytical wave solutions, including hyperbolic, trigonometric, rational, dark, brilliant, combined dark-bright, singular, combined singular, and periodic wave solutions. Additionally, the Adomian decomposition approach is utilized to evaluate the absolute error between analytical and semi-analytical wave solutions. The Hamiltonian system is used to analyze the stability of found solutions to demonstrate their suitability for implementation in the model's application. © 2022

关键词： Adomian decomposition method Hamiltonian system Modified Khater method Perturbed time-fractional nonlinear Schrödinger equation

Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence

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Physical Review Fluids 2020年第5期5卷 054606-054606页

作者： Chenyue Xie Jianchun Wang Weinan E Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Department of Mathematics Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Spatial artificial neural network (ANN) models are developed for subgrid-scale (SGS) forces in the large eddy simulation (LES) of turbulence. The input features are based on the first-order derivatives of the filtered velocity field at different spatial locations. The correlation coefficients of SGS forces predicted by the spatial artifical neural network (SANN) models with reasonable spatial stencil geometry can be made larger than 0.99 in an a priori analysis, and the relative error of SGS forces can be made smaller than 15%, much smaller than that of the traditional gradient model. In a posteriori analysis, a detailed comparison is made on the results of LES using the SANN model, implicit large eddy simulation (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) at grid resolution of 643. It is shown that the SANN model performs better than the ILES, DSM, and DMM models in the prediction of the spectrum and other statistical properties of the velocity field, as well as the instantaneous flow structures. These results suggest that artificial neural network with consideration of spatial characteristics is a very effective tool for developing advanced SGS models in LES of turbulence.

关键词： Compressible flows Turbulence Artificial neural networks

Local two-sample testing over graphs and point-clouds by random-walk distributions

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arXiv 2020年

作者： Landa, Boris Qu, Rihao Chang, Joseph Kluger, Yuval Program in Applied Mathematics Yale University Department of Pathology Yale University School of Medicine Department of Statistics and Data Science Yale University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Immunology Yale School of Medicine

Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two distributions differ. Given samples from two densities f1and f0, we consider the task of localizing occurrences of the inequality f1> f0. To avoid the challenges associated with high-dimensional space, we propose a general hypothesis testing framework where hypotheses are formulated adaptively to the data by conditioning on the combined sample from the two densities. We then investigate a special case of this framework where the notion of locality is captured by a random walk on a weighted graph constructed over this combined sample. We derive a tractable testing procedure for this case employing a type of scan statistic, and provide non-asymptotic lower bounds on the power and accuracy of our test to detect whether f1> f0in a local sense. Furthermore, we characterize the test's consistency according to a certain problem-hardness parameter, and show that our test achieves the minimax detection rate for this parameter. We conduct numerical experiments to validate our method, and demonstrate our approach on two real-world applications: detecting and localizing arsenic well contamination across the United States, and analyzing two-sample single-cell RNA sequencing data from melanoma *** Codes 62G10 Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

Modelling of monthly rainfall patterns in the North-West India using SVM

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Ingenierie des Systemes d'Information 2019年第4期24卷 391-395页

作者： Polisetty, Kalpana Paidipati, Kiran Kumar Bodapati, Jyostna Devi Department of Mathematics Vignan’s Foundation for Science Technology and Research Guntur522213 India Department of Statistics Pondicherry University Puducherry605014 India Department of Computer Science and Engineering Vignan’s Foundation for Science Technology and Research Guntur522213 India

Rainfall forecast is a hotspot in meteorological studies in the last few years. The key difficulty in forecast accuracy lies in the nonlinearity of rainfall data. Considering the potential of support vector machine (SVM) to solve nonlinear time series, this paper develops an SVM-based model based on the monthly rainfall data from 1901 to 2015 in Northwest India. The forecast accuracies of four different kernels were compared, including linear, polynomial, radial basis function (RBF) and sigmoid kernels. The comparison shows that the SVM-based model with the RBF kernel achieved the smallest root mean squared error (RMSE) at the lookback of 25, C=1, γ =0.01 and =0.1. Our research provides an effective tool to predict rainfall in regions with similar meteorological conditions to northwest India. © 2019 International Information and engineering Technology Association. All rights reserved.

关键词： Support vector machines