Locating a complex inhomogeneous medium with an approximate factorization method

Qu, Fenglong; Zhang, Haiwen

doi:10.1088/1361-6420/ab039a

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…Various numerical algorithms have been developed for solving inverse medium scattering problems, such as iterative methods like contrast source-type inversion methods [50,51], iteratively regularized Gauss-Newton method [34], least-squares methods [28], subspace optimization methods [11] and recursive linearization methods with multi-frequencies [5,6,14] and with single frequency [4], which can obtain satisfactory reconstructions while they are generally very time-consuming. Non-iterative methods such as reverse time migrations [10], singular sources methods [43], factorization methods [32,44] and sampling-type methods [8,15,23,26,42] are fast while their reconstructions may not be accurate. We refer to [9,12,20] for more extensive reviews on both theoretical analyses and numerical algorithms on inverse scattering problems.…”

Section: Introductionmentioning

confidence: 99%

A direct sampling-based deep learning approach for inverse medium scattering problems

Ning,

Han,

Zou

2023

Inverse Problems

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In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the eﬃcient direct sampling method (DSM) introduced in [23], we propose a novel direct sampling-based deep learning approach (DSM-DL) for reconstructing inhomogeneous scatterers. In particular, we use the U-Net neural network to learn the relation between the index functions and the true contrasts. Our proposed DSM-DL is computationally eﬃcient, robust to noise, easy to implement, and able to naturally incorporate multiple measured data to achieve high-quality reconstructions. Some representative tests are carried out with varying numbers of incident waves and diﬀerent noise levels to evaluate the performance of the proposed method. The results demonstrate the promising beneﬁts of combining deep learning techniques with the DSM for IMSP.

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Section: Introductionmentioning

confidence: 99%

A direct sampling-based deep learning approach for inverse medium scattering problems

Ning,

Han,

Zou

2023

Inverse Problems

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“…For a comprehensive discussions of regularization methods, see the monographs [15,25] and the references quoted therein. Recently, non-iterative algorithms have attracted much attention in inverse medium scattering problems, such as linear sampling method [13], gap functional method [6], factorization method [28], singular sources method [36] and approximate factorization method [37]. Non-iterative methods do not need to solve the forward problem, and therefore they are computationally fast.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of inhomogeneous media by iterative reconstruction algorithm with learned projector

Li¹,

Zhang²,

Zhang³

2022

Preprint

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This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from an inhomogeneous medium in two dimensions. We propose a deep learningbased iterative reconstruction algorithm for recovering the contrast of the inhomogeneous medium from the far-field data. The proposed algorithm is given by repeated applications of the Landweber method, the iteratively regularized Gauss-Newton method (IRGNM) and a deep neural network. The Landweber method is used to generate initial guesses for the exact contrast, and the IRGNM is employed to make further improvements to the estimated contrast. Our deep neural network (called the learned projector in this paper) mainly focuses on learning the a priori information of the shape of the unknown contrast by using a normalization technique in the training process and is trained to act like a projector which is expected to make the estimated contrast obtained by the Landweber method or the IRGNM closer to the exact contrast. It is believed that the application of the normalization technique can release the burden of training the deep neural network and lead to good performance of the proposed algorithm. Furthermore, the learned projector is expected to provide good initial guesses for IRGNM and be helpful for accelerating the proposed algorithm. Extensive numerical experiments show that our inversion algorithm has a satisfactory reconstruction capacity and good generalization ability.

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“…Numerical examples are also carried out to demonstrate the effectiveness of the inversion algorithm. It should be remarked that an approximate factorization or asymptotic factorization method has also been studied for inverse scattering problems with phased data (see [3,19,20,50,51]). To the best of our knowledge, the present paper is the first attempt to employ the idea of the factorization method in inverse scattering problems with phaseless data.…”

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An approximate factorization method for inverse acoustic scattering with phaseless total-field data

Zhang¹,

Zhang²

2019

Preprint

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This paper is concerned with the inverse acoustic scattering problem with phaseless near-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the unknown scatterer from the phaseless near-field data generated by incident plane waves at a fixed frequency and measured on the circle ∂B R with a sufficiently large radius R. The theoretical analysis of our method is based on the asymptotic property in the operator norm from H 1/2 (S 1 ) to H −1/2 (S 1 ) of the phaseless near-field operator defined in terms of the phaseless near-field data measured on ∂B R with large enough R, where H s (S 1 ) is a Sobolev space on the unit circle S 1 for real number s, together with the factorization of a modified far-field operator. The asymptotic property of the phaseless near-field operator is also established in this paper with the theory of oscillatory integrals. The unknown scatterer can be either an impenetrable obstacle of sound-soft, sound-hard or impedance type or an inhomogeneous medium with a compact support, and the proposed inversion algorithm does not need to know the boundary condition of the unknown obstacle in advance. Numerical examples are also carried out to demonstrate the effectiveness of our inversion method. To the best of our knowledge, it is the first attempt to develop a factorization type method for inverse scattering problems with phaseless data.

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Locating a complex inhomogeneous medium with an approximate factorization method

Cited by 7 publications

References 32 publications

A direct sampling-based deep learning approach for inverse medium scattering problems

A direct sampling-based deep learning approach for inverse medium scattering problems

Reconstruction of inhomogeneous media by iterative reconstruction algorithm with learned projector

An approximate factorization method for inverse acoustic scattering with phaseless total-field data

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