Fast acoustic source imaging using multi-frequency sparse data

Alzaalig, Ala; Hu, Guanghui; Liu, Xiaodong; Sun, Jiguang

doi:10.1088/1361-6420/ab4aec

Cited by 43 publications

(51 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The following theorem gives a uniqueness result on determine the strip by using only compressional far field data or shear far field data at a fixed observation direction. The proof follows the related results for inverse acoustic source scattering problems [1]. Theorem 3.5.…”

Section: Scattering Of Sourcesmentioning

confidence: 60%

See 1 more Smart Citation

Inverse elastic scattering problems with phaseless far field data

Liu

2019

Inverse Problems

Self Cite

View full text Add to dashboard Cite

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. The phaseless far field data is closely related to the outward energy flux, which is easily measured in practice. Systematically, we study two basic models, i.e., inverse scattering of plane waves by rigid bodies and inverse scattering of sources with compact support. For both models, we show that the phaseless far field data is invariant under translation of the underlying scattering objects, which implies that the location of the objects can not be uniquely recovered by the data. To solve this problem, we consider simultaneously the incident point sources with one fixed source point and at most three scattering strengths. With this technique, we establish some uniqueness results for source scattering problem with multi-frequency phaseless far field data. Furthermore, a fast and stable phase retrieval approach is proposed based on a simple geometric result which provides a stable reconstruction of a point in the plane from three distances to given points. Difficulties arise for inverse scattering by rigid bodies due to the additional unknown far field pattern of the point sources. To overcome this difficulty, we introduce an artificial rigid body into the system and show that the underlying rigid bodies can be uniquely determined by the corresponding phaseless far field data at a fixed frequency. Noting that the far field pattern of the scattered field corresponding to point sources is very small if the source point is far away from the scatterers, we propose an appropriate phase retrieval method for obstacle scattering problems, without using the artificial rigid body. Finally, we propose several sampling methods for shape reconstruction with phaseless far field data directly. For inverse obstacle scattering problems, two different direct sampling methods are proposed with data at a fixed frequency. For inverse source scattering problems, we introduce two direct sampling methods for source supports with sparse multi-frequency data. The phase retrieval techniques are also combined with the classical sampling methods for the shape reconstructions. Extended numerical examples in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval techniques and sampling methods.the readers interested in a more comprehensive treatment of the direct and inverse elastic scattering problems, we suggest consulting [9,14,36,37] on this subject.The two well known difficulties of the inverse scattering problems are nonlinearity and ill-posedness. Actually, in many cases of practical interest, the third difficulty is incomplete data, i.e., only partial information can be measured directly. There are two cases of incomplete data. The first one is the limited-aperture data, where the measurements are only available in limited directions or positions. Limited-aperture data can present a severe ch...

show abstract

Section: Scattering Of Sourcesmentioning

confidence: 60%

“…Phaseless inverse source problems. The forward problems are computed the same as in [1]. In all examples, forx ∈ Θ, we consider multiple frequency far field data u ∞ F,s (x, k j ), j = 1, · · · , N, where N = 20, k min = 0.5, k max = 20 such that k j = (j − 0.5)∆k, ∆k = kmax N .…”

Section: 2mentioning

confidence: 99%

Inverse elastic scattering problems with phaseless far field data

Liu

2019

Inverse Problems

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the last decades, great efforts had been devoted to the numerical methods for the inverse source problem of determining an acoustic source. We refer interested readers to [3,7,9,22,23,25,27] for the sampling method, the continuation method, the eigenfunction expansion method and the Fourier method for recovering the static sources and [20,21] for the investigations on imaging the moving point sources.…”

Section: Introductionmentioning

confidence: 99%

Retrieval of acoustic sources from multi-frequency phaseless data

Zhang

Guo

et al. 2018

Inverse Problems

View full text Add to dashboard Cite

We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering the phase information of far-field data. This reference source technique leads to an easy-to-implement phase retrieval formula. Mathematically, the stability of the phase retrieval approach is rigorously justified. Then we employ the Fourier method to deal with the multi-frequency inverse source problem with recovered phase information. Finally, some two and three dimensional numerical results are presented to demonstrate the viability and effectiveness of the proposed method.

show abstract

“…Recently in [26], it is shown that the maximum and minimum distance between measurement point and the support of the source can be uniquely determined by using the electric field at a single point. The idea is from [1,23,39] for inverse acoustic source problem with multi-frequency sparse far field data.…”

mentioning

confidence: 99%

“…We first give a uniqueness result following the ideas for the inverse acoustic and elastic scattering problems [1,28].…”

mentioning

confidence: 99%

Inverse Electromagnetic Source Scattering Problems with MultiFrequency Sparse Phased and Phaseless Far Field Data

Ji¹,

Liu²

2019

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data, we show that the smallest strip containing the source support with the observation direction as the normal can be uniquely determined by the multi-frequency far field pattern at a single observation direction. A phased direct sampling method is also proposed to reconstruct the strip. The phaseless far field data is closely related to the outward energy flux, which can be measured more easily in practice. We show that the phaseless far field data is invariant under the translation of the sources, which implies that the location of the sources can not be uniquely recovered by the data. To solve this problem, we consider simultaneously the scattering of magnetic dipoles with one fixed source point and at most three scattering strengths. With this technique, a fast and stable phase retrieval approach is proposed based on a simple geometrical result which provides a stable reconstruction of a point in the plane from three distances to the given points. A novel phaseless direct sampling method is also proposed to reconstruct the strip. The phase retrieval approach can also be combined with the phased direct sampling method to reconstruct the strip. Finally, to obtain a source support, we just need to superpose the indicators with respect to the sparse observation directions. Extended numerical examples in three dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval approach and direct sampling methods.

show abstract

Fast acoustic source imaging using multi-frequency sparse data

Cited by 43 publications

References 21 publications

Inverse elastic scattering problems with phaseless far field data

Inverse elastic scattering problems with phaseless far field data

Retrieval of acoustic sources from multi-frequency phaseless data

Inverse Electromagnetic Source Scattering Problems with MultiFrequency Sparse Phased and Phaseless Far Field Data

Contact Info

Product

Resources

About