- 标题
- 摘要
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- 实验方案
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A method of solving the coefficient inverse problems of wave tomography
摘要： In this paper, the problem of nonlinear wave tomography is formulated as a coefficient inverse problem for a hyperbolic equation in the time domain. Efficient methods for solving the inverse problems of wave tomography for the case of transparent boundary conditions are presented. The algorithms are designed for supercomputers. We prove the Fréchet differentiability theorem for the residual functional and derive an exact expression for the Fréchet derivative in the case of a transparent boundary in the direct and conjugate problems. The expression for the Fréchet derivative of the residual functional remains valid if the experimental data are provided for only a part of the boundary. The effectiveness of the proposed method is illustrated by the numerical solution of a model problem of low-frequency wave tomography. The model problem is tailored to apply to the differential diagnosis of breast cancer.
关键词： Coefficient inverse problems,Wave tomography,Wave equation,Fréchet derivative,Supercomputer,Transparent boundary conditions
更新于2025-09-09 09:28:46
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Inverse of Affine Radon Transform for Light Field Reconstruction from Focal Stack
摘要： The light ?eld can be applied to computational imaging methods such as digital refocusing, depth reconstruction and all-in-focus imaging. In this paper, the af?ne Radon transform of generating the focal stack by the light ?eld is proposed. Then we derive the inverse formula of af?ne Radon transform for reconstructing the light ?eld from the focal stack. We analyze the ill-posedness of the reconstruction problem by the inversion formula and the incompleteness of the focal stack data. The inversion formula reveals the instability of the solution. The focal stack can be regarded as the incomplete data for light ?eld reconstruction in the spatial domain, while it corresponds to the limited support of light ?eld in the Fourier domain. The numerical solution of light ?eld reconstruction is realized by approximating the inverse of af?ne Radon transform. Based on the approximated inverse af?ne Radon transform of light ?eld reconstruction, the high-precision light ?eld data reconstruction method and the computational imaging method can be established via the focal stack data. The experimental results show that the high-precision light ?eld can be reconstructed from focal stack based on the approximated inverse af?ne Radon transform.
关键词： light ?eld,focal stack,af?ne Radon transform,inverse problems
更新于2025-09-09 09:28:46
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Unique Solvability of the Three-Dimensional Inverse Problem of Electromagnetic Sounding
摘要： The article considers a three-dimensional inverse problem to determine the conductivity distribution in a three-dimensional body embedded in a layered conducting medium. A uniqueness theorem is proved for the class of layered bodies with finitely many layers where conductivity is observed only in the direction of the layer.
关键词： electromagnetic sounding,inverse problems,solution uniqueness
更新于2025-09-04 15:30:14
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Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications
摘要： In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large number of singular values and vectors more efficiently than other well-known schemes, such as iterative algorithms based on Golub–Kahan–Lanczos bidiagonalization. We provide theoretical results and numerical experiments to demonstrate the accuracy of our approximation and show how the approximation can be used to solve large scale ill-posed inverse problems, either as an approximate filtering method, or as a preconditioner to accelerate iterative algorithms.
关键词： regularization,inverse problems,image restoration,SVD,image reconstruction,Kronecker products
更新于2025-09-04 15:30:14
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[Institution of Engineering and Technology 12th European Conference on Antennas and Propagation (EuCAP 2018) - London, UK (9-13 April 2018)] 12th European Conference on Antennas and Propagation (EuCAP 2018) - On the Use of the Source Reconstruction Method for Metasurface Design
摘要： This paper aims to facilitate the macroscopic design of radiation-controlling metasurfaces with the goal of satisfying specific far-field performance criteria rather than a desired field or power patten. The source reconstruction method, a well-developed technique for antenna measurements, is modified to accept a collection of far-field performance criteria. Solving the resulting nonlinear inverse source problem results in a set of electric and magnetic currents that directly relate to tangential fields required for established metasurface design methods. The proposed technique is presented along with a preliminary example demonstrating the capabilities of the basic framework.
关键词： metasurface design,source reconstruction method (SRM),inverse problems,antenna design
更新于2025-09-04 15:30:14