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Non-Linear Reconstruction for ERT Inverse Problem Based on homotopy algorithm

IEEE SENSORS JOURNAL 2023年第10期23卷 10404-10412页

作者： Zhang, Wei Tan, Chao Dong, Feng Hebei Univ Technol Sch Artificial Intelligent & Data Sci Tianjin 300130 Peoples R China Tianjin Univ Sch Elect & Informat Engn Tianjin Key Lab Proc Measurement & Control Tianjin 300072 Peoples R China

Due to the non-linear and non-convex properties, classical electrical resistance tomography (ERT) image reconstruction algorithms are less effective and less accurate. In this article, a non-linear and non-convex image reconstruction algorithm based on the homotopy method was proposed. The proposed algorithm converted the ERT inverse problem to a multi-object non-convex optimization which promoted the reconstruction accuracy and avoid the local optimal. Experimental validations were conducted. The optimization process is studied which demonstrates its effectiveness. Moreover, the proposed algorithm is compared with six other representative algorithms (linear/non-linear and convex/non-convex) at the condition of different distributions and the number of objects. The image quality parameters of the proposed algorithms are studied which show that the homotopy algorithm can provide image reconstruction result with higher quality and better stability than the other conventional algorithms.

关键词： Matching pursuit algorithms Image reconstruction Inverse problems Optimization Mathematical models Approximation algorithms Convergence Compressed sensing electrical resistance tomography (ERT) homotopy algorithm inverse problem non-convex optimization

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A fast homotopy algorithm for gridless sparse recovery

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INVERSE PROBLEMS 2021年第2期37卷

作者： Courbot, Jean-Baptiste Colicchio, Bruno IRIMAS UR 7499 61 Rue Albert Camus F-68100 Mulhouse France

In this paper, we study the solving of the gridless sparse optimization problem and its application to 3D image deconvolution. Based on the recent works of [14] introducing the sliding Frank-Wolfe algorithm to solve the Beurling LASSO problem, we introduce an accelerated algorithm, denoted BSFW, that preserves its convergence properties, while removing most of the costly local descents. Besides, as the solving of BLASSO still relies on a regularization parameter, we introduce a homotopy algorithm to solve the constrained BLASSO that allows to use a more practical parameter based on the image residual, e.g. its standard deviation. Both algorithms benefit from a finite termination property, i.e. they are guaranteed to find the solution in a finite number of step under mild conditions. These methods are then applied on the problem of 3D tomographic diffractive microscopy images, with the purpose of explaining the image by a small number of atoms in convolved observations. Numerical results on synthetic and real images illustrates the improvement provided by the BSFW method, the homotopy method and their combination.

关键词： Beurling LASSO gridless sparse optimization homotopy algorithm 3D deconvolution tomographic diffractive microscopy

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Research on Six Degrees of Freedom Magnetic Positioning Method based on homotopy algorithm 3

Research on Six Degrees of Freedom Magnetic Positioning Meth...

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3rd IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)

作者： Xue, Jing Zhao, Jianhui Li, Fan Beihang Univ Sch Instrumentat Sci & Optoelect Engn Beijing Peoples R China

ISBN: (纸本)9781538645093

Electromagnetic positioning technology based on excitation coils can achieve rapid and high precision positioning in a short distance area. However, the efficiency and accuracy are low in a long distance area. In order to improve the efficiency of the long distance magnetic positioning, a magnetic positioning method based on homotopy algorithm is proposed. Three orthogonal coils are excited separately to generate the magnetic field, and a three-axis fluxgate sensor is mounted on the target object to measure the magnetic field. Then the homotopy algorithm is chosen to solve the nonlinear equations of the magnetic field. The effectiveness of the algorithm is verified by experiments. The algorithm runs no more than 1 second at a time and the maximum positioning error does not exceed 0.5 meters within four meters.

关键词： electromagnetic positioning homotopy algorithm magnetic field nonlinear equations

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Globally convergent homotopy algorithm for solving the KKT systems to the principal-agent bilevel programming

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OPTIMIZATION METHODS & SOFTWARE 2017年第1期32卷 69-85页

作者： Zhu, Zhichuan Yu, Bo Northeast Normal Univ Sch Math & Stat Changchun 130024 Jilin Peoples R China Jilin Univ Finance & Econ Fac Stat Changchun 130117 Jilin Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Liaoning Peoples R China

In this paper, a constraint set swelling homotopy (CSSH) algorithm for solving the single-level non-convex programming problem with designing piecewise linear contractual function which is equivalent to the principal-agent model with integral operator is proposed, and the existence and global convergence is proven under some mild conditions. As a comparison, a piecewise constant contract is also designed for solving the single-level non-convex programming problem with the corresponding discrete distributions. And some numerical tests are done by the proposed homotopy algorithm as well as by using fmincon in Matlab, LOQO and MINOS. The numerical results show that the CSSH algorithm is robust, feasible and effective.

关键词： principal-agent model homotopy algorithm bilevel programming non-convex programming

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Sparse diffraction imaging method using an adaptive reweighting homotopy algorithm

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JOURNAL OF GEOPHYSICS AND ENGINEERING 2017年第1期14卷 26-40页

作者： Yu, Caixia Zhao, Jingtao Wang, Yanfei Qiu, Zhen Chinese Acad Sci Inst Geol & Geophys Key Lab Petr Resources Res Beijing 100029 Peoples R China China Univ Min & Technol Beijing State Key Lab Coal Resources & Safe Min Beijing 100083 Peoples R China PetroChina Res Inst Petr Explorat & Dev Beijing 100083 Peoples R China

Seismic diffractions carry valuable information from subsurface small-scale geologic discontinuities, such as faults, cavities and other features associated with hydrocarbon reservoirs. However, seismic imaging methods mainly use reflection theory for constructing imaging models, which means a smooth constraint on imaging conditions. In fact, diffractors occupy a small account of distributions in an imaging model and possess discontinuous characteristics. In mathematics, this kind of phenomena can be described by the sparse optimization theory. Therefore, we propose a diffraction imaging method based on a sparsityconstraint model for studying diffractors. A reweighted L-2-norm and L-1-norm minimization model is investigated, where the L-2 term requests a least-square error between modeled diffractions and observed diffractions and the L-1 term imposes sparsity on the solution. In order to efficiently solve this model, we use an adaptive reweighting homotopy algorithm that updates the solutions by tracking a path along inexpensive homotopy steps. Numerical examples and field data application demonstrate the feasibility of the proposed method and show its significance for detecting small-scale discontinuities in a seismic section. The proposed method has an advantage in improving the focusing ability of diffractions and reducing the migration artifacts.

关键词： diffraction imaging sparsity-constraint model homotopy algorithm

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homotopy algorithm for l1-norm minimisation problems

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IET SIGNAL PROCESSING 2015年第1期9卷 1-9页

作者： Dai, Jisheng Xu, Weichao Zhang, Jin Chang, Chunqi Jiangsu Univ Sch Elect & Informat Engn Zhenjiang 212013 Peoples R China Guangdong Univ Technol Sch Automat Dept Automat Control Guangzhou 510006 Guangdong Peoples R China Hefei Elect Engn Inst Dept Elect & Elect Engn Hefei 230027 Peoples R China Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China

This paper proposes a novel approach to handle the singularity problem in the homotopy algorithm. Following a state-of-art ridge-adding-based method, the authors introduce a random ridge term to each element of the measure matrix to avoid the occurrence of singularities. Then, the authors give the sufficient condition of avoiding singularities, and prove that adding random ridge is greatly useful to deal with the singularity problem, even the random ridge tends to zero. Although the main procedures in the method coincide with the state-of-art method, all the derivations and theoretical analyses are different because of distinct forms of optimisation problems. Thus, this work is by no means a trivial task. Moreover, the authors note that the most computationally expensive step in the proposed method is the inversion of active matrices, whose time complexity relative to that of other required operations is proportional to the active set's cardinality. This motivates us to develop an efficient QR update algorithm based on the new ridge-adding-based method, which is incorporated in Givens QR factorisation and Gaussian elimination. It turns out that, with such new QR update algorithm, the previous ratio of time complexities can be reduced to a constant order. As a consequence, the new method can eliminate the bottleneck of matrix inversion in the improved homotopy algorithm.

关键词： minimisation matrix algebra Gaussian processes homotopy algorithm l1 -norm minimisation problems singularity problem state-of-art ridge adding based method matrix measurement optimisation problems active matrices ridge adding based method Gaussian elimination matrix inversion

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Darcy-Forchheimer mangetized flow based on differential type nanoliquid capturing Ohmic dissipation effects

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Propulsion and Power Research 2023年第3期12卷 443-455页

作者： M.Waqas Yunjie Xu M.Nasir Md Mottahir Alam Amjad Ali Pasha Kashif Irshad Bandar M.Fadhl M.S.Kausar NUTECH School of Applied Science and Humanities National University of TechnologyIslamabad 44000Pakistan Department of Mechanical Engineeing Lebanese American UniversityBeirutLebanon School of Engineering Huzhou UniversityHuzhou 313000China Faculty of Informatics and Computing University Sultan Zainal AbidinBesut Campus22200 BesutTereng-ganuMalaysia Department of Electrical and Computer Engineering King Abdulaziz UniversityJeddah 21589Saudi Arabia Aerospace Engineering Department King Abdulaziz UniversityJeddah 21589Saudi Arabia Interdisciplinary Research Centre for Renewable Energy and Power System(IRC-REPS) Research InstituteKing Fahd University of Petroleum and Minerals(KFUPM)Dhahran 31261Saudi Arabia Mechanical Engineering Department College of Engineering and Islamic ArchitectureUmm Al-Qura UniversityP.O.Box 5555Makkah 21955Saudi Arabia

Hydromagnetic nanoliquid establish an extraordinary category of nanoliquids that unveil both liquid and magnetic *** interest in the utilization of hydromagnetic nanoliquids as a heat transporting medium stem from a likelihood of regulating its flow along with heat transportation process subjected to an externally imposed magnetic *** analysis reports the hydromagnetic nanoliquid impact on differential type(second-grade)liquid from a convectively heated extending *** well-known Darcy-Forchheimer aspect capturing porosity characteristics is introduced for nonlinear *** conditions elaborating heat-mass transportation effect are *** addition,Ohmic dissipation and suction/injection aspects are also a part of this *** analysis is done by implementing the basic relations of fluid *** modeled physical problem is simplified through order *** resulting systems(partial differential expressions)are rendered to the ordinary ones by utilizing the apposite *** solutions are constructed employing homotopy *** and numeric result are addressed comprehensively to elaborate the nature of sundry parameters against physical *** velocity profile is suppressed with increasing Hartmann number(magnetic parameter)whereas it is enhanced with increment in material parameter(second-grade).With the elevation in thermophoresis parameter,temperature and concentration of nanoparticles are accelerated.

关键词： Darcy-Forchheimer magnetized flow Differential type nanoliquid Ohimc dissipation Robin conditions homotopy algorithm

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Applications of homotopy algorithm for Solving Optimal Power Flow of Power system

Applications of Homotopy Algorithm for Solving Optimal Power...

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International Symposium on Vehicle, Mechanical, and Electrical Engineering (ISVMEE 2013)

作者： ZHang, Xiaoying Ding, Ning Li, Chen Lanzhou Univ Technol Sch Elect & Informat Engn Lanzhou 730050 Peoples R China

ISBN: (纸本)9783038350033

This paper introduces an homotopy algorithm which has convergence stability to solve the alternating current optimal power flow problem. The complicated Alternating Current Power Flow (ACPF) can simplify as simple Direct Current Power Flow (DCPF). The homotopy participation factor is introduced into the linear DCPF to make DCPF convert back into ACPF gradually to realize Alternating Current Power Flow homotopy method (ACPFH). The homotopy curves are generated to solve a series of nonlinear *** traditional method can not solve the unstable points,because the calculate process always turn up Jacobian *** the homotopy method can calculate all results. It is a superiority for homotopy,and then can explore power system problem more *** novel algorithm is different from Newton - Raphson method, because it isn't sensitive to the initial point selection and has the global *** homotopy algorithm is applied to IEEE - 3, 9, 14, 30, 36, 57, 118 node testing systems for power flow optional calculation, the simulation results show that the novel algorithm can solve power flow problem better and its calculating speed is much faster than the traditional algorithm, it can calculate the optimal value more direct.

关键词： convergence homotopy algorithm Newton-Raphson method optimal power flow nonlinear

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Soft homotopy through Moore-Penrose Inverse 10

Soft Homotopy through Moore-Penrose Inverse

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10th IEEE International Conference on Computational Intelligence and Virtual Environments for Measurement Systems and Applications (IEEE CIVEMSA)

作者： Tausiesakul, Bamrung Srinakharinwirot Univ Dept Elect Engn Fac Engn 63 Mu 7Rangsit Nakhonnayok RdCanal 16 Nakhonnayok 26120 Thailand

ISBN: (数字)9781665434454

ISBN: (纸本)9781665434454

The acquisition of a discrete-time signal is an important part of a compressive sensing problem. A fine algorithm that could bring better signal recovery performance is often called for. In this work, two homotopy algorithms that involve a soft thresholding decision are proposed using the Moore-Penrose inverse. The additional complexity required in the two proposed methods is relatively minimal, since the necessary matrix inverse (AA(inverted perpendicular)) and the matrix multiplication A(inverted perpendicular) (AA(inverted perpendicular))(-1) can be done before the iteration starts, where. (inverted perpendicular) is the transpose. Numerical examples illustrate the improved error performance for different values of the shrinking parameter gamma. It is found that the greater the shrinking parameter, the less the signal recovery error one could obtain from the two new approaches.

关键词： Compressive sensing homotopy algorithm soft thresholding

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A homotopy Approach to Coherent Quantum LQG Control Synthesis Using Discounted Performance Criteria 24

A Homotopy Approach to Coherent Quantum LQG Control Synthesi...

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24th International Symposium on Mathematical Theory of Networks and Systems (MTNS)

作者： Vladimirov, Igor G. Petersen, Ian R. Australian Natl Univ Coll Engn & Comp Sci Res Sch Elect Energy & Mat Engn Canberra ACT 2601 Australia

This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of a plant and a coherent (measurement-free) controller. The plant and controller are multimode open quantum harmonic oscillators governed by linear quantum stochastic differential equations. The control objective is to make the closed-loop system internally stable and to minimize the infinite-horizon quadratic cost for the plant variables and the controller output subject to quantum physical realizability (PR) constraints. This coherent quantum LQG (CQLQG) control problem, which has been of active research interest for over ten years, does not admit a solution in the form of separation principle and independent Riccati equations known for its classical counterpart. We apply variational techniques to a family of discounted CQLQG control problems parameterized by an effective time horizon. This yields a homotopy algorithm, which is initialized with a PR (but not necessarily stabilizing) controller and aims at a locally optimal stabilizing controller for the original problem in the limit. Copyright (C) 2021 The Authors.

关键词： Open quantum harmonic oscillator coherent quantum feedback discounted quadratic cost homotopy algorithm

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