On an artificial neural network for inverse scattering problems

Gao, Yu; Liu, Hongyu; Wang, Xianchao; Zhang, Kai

doi:10.1016/j.jcp.2021.110771

Cited by 50 publications

(14 citation statements)

References 31 publications

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“…Similar problems are of great practical importance. It was mentioned above that there are extensive studies devoted to the study of equations of the form (56). They considered either linearized equations or nonlinear approximations of Equation (56).…”

Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

“…Below we demonstrate Hopfield neural networks for solving the original Equation (56). Let ∆ k , k = 0, 1, .…”

Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

“…First, the authors started to study the amplitude-phase problem [52,53]. Second, a couple of works devoted to applications of neural networks for inverse problems of restoration have been published recently [55,56]. It is of interest to investigate the possible use of the continuous operator method application for these issues.…”

mentioning

confidence: 99%

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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Roudnev

Boykova

2022

Mathematics

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A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks’ stability defined via coefficients of systems of differential equations.

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Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

“…Below we demonstrate Hopfield neural networks for solving the original Equation (56). Let ∆ k , k = 0, 1, .…”

Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Roudnev

Boykova

2022

Mathematics

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“…With the increasing antennas at the base station (BS) in the mm Wave massive MIMO communication system, severe problems of complex matrix inverse operation and huge pilot overhead are produced. There are some recent works addressing the wave imaging on the machine-learning approach [ 26 , 27 , 28 ]. Motivated by the methods mentioned above, we regard the quantized received measurements at the BS as a low-resolution image and adopt a state-of-the-art channel estimation framework based on residual learning and multi-path feature fusion to reconstruct the mm Wave channel accurately.…”

Section: Introductionmentioning

confidence: 99%

Residual Learning and Multi-Path Feature Fusion-Based Channel Estimation for Millimeter-Wave Massive MIMO System

Zheng

Liu

Liang

et al. 2022

Entropy

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Channel estimation is a challenging task in a millimeter-wave (mm Wave) massive multiple-input multiple-output (MIMO) system. The existing deep learning scheme, which learns the mapping from the input to the target channel, has great difficulty in estimating the exact channel state information (CSI). In this paper, we consider the quantized received measurements as a low-resolution image, and we adopt the deep learning-based image super-resolution technique to reconstruct the mm Wave channel. Specifically, we exploit a state-of-the-art channel estimation framework based on residual learning and multi-path feature fusion (RL-MFF-Net). Firstly, residual learning makes the channel estimator focus on learning high-frequency residual information between the quantized received measurements and the mm Wave channel, while abundant low-frequency information is bypassed through skip connections. Moreover, to address the estimator’s gradient dispersion problem, a dense connection is added to the residual blocks to ensure the maximum information flow between the layers. Furthermore, the underlying mm Wave channel local features extracted from different residual blocks are preserved by multi-path feature fusion. The simulation results demonstrate that the proposed scheme outperforms traditional methods as well as existing deep learning methods, especially in the low signal-to-noise-ration (SNR) region.

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“…It is also interesting to note the similarity shared by our method and the machine learning approaches for inverse obstacle problems. In [12,35], machine learning approaches were developed that can yield a highly-accurate reconstruction of a target obstacle by using only a few far-field measurements. However, a large amount of data as well as computations are needed to train the neural networks therein, and hence are computationally more costly.…”

Section: Introductionmentioning

confidence: 99%

A novel quantitative inverse scattering scheme using interior resonant modes

He¹,

Liu²,

Wang³

2022

Preprint

Self Cite

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This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown obstacle from the far-field data via the indicating behaviour of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme of Newton's type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton's iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the Newton's formula involves the geometric quantities of the unknown boundary surface in a natural way. We provide rigorous theoretical justifications of the proposed method. Numerical experiments in both 2D and 3D are conducted, which confirm the promising features of the proposed imaging scheme. In particular, it can produce quantitative reconstructions of high accuracy in a very efficient manner.

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On an artificial neural network for inverse scattering problems

Cited by 50 publications

References 31 publications

Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Residual Learning and Multi-Path Feature Fusion-Based Channel Estimation for Millimeter-Wave Massive MIMO System

A novel quantitative inverse scattering scheme using interior resonant modes

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