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A Method for Solving the inverse scattering problem for Shape and Impedance of Crack

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Numerical Mathematics(Theory,Methods and Applications) 2013年第2期6卷 343-352页

作者： Ali Yang Liantang Wang Xiaohua Li School of Science Xi’an Polytechnic UniversityXi’an 710048ShannxiChina Mathematics Department of Northwest University Xi’an 710069ShannxiChina School of Science Xi’an University of Science and TechnologyXi’an 710054ShannxiChina

The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in *** combined single-and double-layer potential is used to approach the scattered *** an important feature,this method does not require the solution of u and δu/δv at each *** approximate method is presented and the convergence of this method is *** examples are given to show that this method is both accurate and simple to use.

关键词： Impedance boundary condition Helmholtz equation inverse scattering problem

A Regularized Newton Method in inverse scattering problem from Cavities

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Northeastern Mathematical Journal 2007年第6期23卷 479-490页

作者：冯立新马富明 School of Mathematical Sciences Heilongjiang University Institute of Mathematics Jilin University

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization. For its approximate solution we propose a regularized Newton iteration scheme. For a foundation of Newton type methods we establish the Fr^chet differentiability of solution to the scattering problem with respect to the boundary of the cavity. Some numerical examples of the feasibility of the method are presented.

关键词： inverse scattering problem regularization Newton method

Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

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Chinese Physics B 2018年第10期27卷 130-140页

作者： Xue Qin School of Mathematical Sciences Peking UniversityBeijing 100871China

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.

关键词： factorization method planar waveguide inverse scattering problem

inverse Electromagnetic scattering by a Penetrable Chiral Object

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Journal of Applied Mathematics and Physics 2024年第9期12卷 3081-3098页

作者： Sotiria Dimitroula Paraskevi Roupa Spyridon C. Athanasiadis Georgios Halikias Department of Mathematics National and Kapodistrian University of Athens Athens Greece Department of Informatics and Telecommunications National and Kapodistrian University of Athens Athens Greece School of Electrical and Computer Engineering National and Technical University of Athens Athens Greece

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.

关键词： Chiral Media inverse scattering problem Chiral Mixed Reciprocity Relation

Microwave Through Wall Imaging via An Induced Current Learning Method

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Journal of Beijing Institute of Technology 2024年第3期33卷 248-254页

作者： Pengjin Lan Jianguo Huang Tianyi Zhou Faculty of Electrical Engineering and Computer Science Ningbo UniversityNingbo 315211China

In this paper,an induced current learning method(ICLM)for microwave through wall imaging(TWI),named as TWI-ICLM,is *** the inversion of induced current,the unknown object along with the enclosed walls are treated as a combination of ***,a non-iterative method called distorted-Born backpropagation(DB-BP)is utilized to generate the initial *** the training stage,several convolutional neural networks(CNNs)are cascaded to improve the estimated induced *** addition,a hybrid loss function consisting of the induced current error and the permittivity error is used to optimize the network ***,the relative permittivity images are conducted analytically using the predicted current based on *** the numerical and experimental TWI tests prove that,the proposed method can achieve better imaging accuracy compared to traditional distorted-Born iterative method(DBIM).

关键词： through wall imaging inverse scattering problem convolutional neural network(CNN)

Broad Learning System with Preprocessing to Recover the scattering Obstacles with Far-Field Data

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Advances in Applied Mathematics and Mechanics 2023年第4期15卷 984-1000页

作者： Weishi Yin Hongyu Qi Pinchao Meng Changchun University of Science and Technology ChangchunJilin 30000China

Based on Broad Learning System with preprocessing,the impenetrable obstacles were ***,the far-field data were preprocessed by Random Forest,and the shapes of the obstacles were classified by dividing the far-field data into different ***,the broad learning system was employed for reconstructing the unknown *** far-field data of the scatterer were regarded as the input nodes of mapped features in the network,and all the mapped features were connected with the enhancement nodes of random weights to the output ***,the coefficient of the output can be obtained by the *** method for the recovery of the scattering obstacles is named ***,numerical experiments revealed that the proposed method is effective,and that the training speed was significantly improved,compared with the deep learning method.

关键词： inverse scattering problem broad learning system machine learning random forest

THE RECONSTRUCTION OF OBSTACLES IN A WAVEGUIDE USING FINITE ELEMENTS

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Journal of Computational Mathematics 2018年第1期36卷 29-46页

作者： Ruming Zhang Jiguang Sun Department of Mathematical Sciences Michigan Technological University Michigan USA

This paper concerns the reconstruction of a penetrable obstacle embedded in a waveg- uide using the scattered data due to point sources, which is formulated as an optimization problem. We propose a fast reconstruction method based on a carefully designed finite element scheme for the direct scattering problem. The method has several merits： 1） the linear sampling method is used to quickly obtain a good initial guess; 2） finite Fourier series are used to approximate the boundary of the obstacle, which is decoupled from the boundary used by the finite element method; and 3） the mesh is fixed and hence the stiff- ness matrix, mass matrix, and right hand side are assembled once and only minor changes are made at each iteration. The effectiveness of the proposed method is demonstrated by numerical examples.

关键词： inverse scattering problem Waveguides Finite element method.

Study of extracting characteristic parameters from a blood vessel

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Chinese Journal of Acoustics 1995年第2期14卷 179-185页

作者： WANG Rcnqian CHEN Yijuan and LI Yingchun(Radio Electronics Department, Peking University, Beijing 100871)(State Key Laboratory of Acoustics. Academia Sinica, Beijing 100080)

A geometrical acoustical method was used to describe the scattered ficld of a softtube (simulating a blood vessel). inverse scattering problem of the soft-tube in the space domain and frequency domain was discussed. The scattered field was measured and the internal radius, external radius, velocity, density and attenuahon coefficient of the tube were reconstructed. The relative deviations were less than 5 %.

关键词： inverse scattering problem Blood vessel

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一个声波散射区域的重建方法与唯一性定理

Northeastern Mathematical Journal 1996年第3期12卷 319-327页

作者：王连堂

The reconstruction of scattering domain of acoustic waves is studied in this paper and two uniqueness theorems for the scattering domains determined by incident waves with different wave numbers are established. A novel method in reconstructing the scattering obstacles with near field data is proposed. The theoretical basis in mathematics of the method and the convergence results are rigorously demonstrated.

关键词： inverse scattering problem scattering Domain Uniqueness Theorem