Fast acoustic source imaging using multi-frequency sparse data

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

doi:10.48550/arxiv.1712.02654

Cited by 10 publications

(20 citation statements)

References 1 publication

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“…Acoustic source imaging problems play an important role in such diverse areas as antenna synthesis, biomedical imaging, sound source localization, or identification of pollutant in the environment. In the last forty years, the inverse acoustic source scattering problems have attracted more and more attention, and significant progress has been made on uniqueness [1,2,6,8,9,10,11,12,15], stability analyses [2,3,7,10,11,13] and numerical approaches [1,2,3,5,10,11,12,16,17].…”

Section: Introductionmentioning

confidence: 99%

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Liu

Zhang

2019

Journal of Computational Physics: X

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Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the underlying sources. Furthermore, the phaseless far field pattern is also invariant if the source is multiplied by any complex number with modulus one. Therefore, the source can not be uniquely determined, even the multifrequency phaseless far field patterns are considered. By adding a reference point source into the model, we propose a simple and stable phase retrieval method and establish several uniqueness results with phaseless far field data. We proceed to introduce a novel direct sampling method for shape and location reconstruction of the source by using broadband sparse phaseless data directly. We also propose a combination method with the novel phase retrieval algorithm and the classical direct sampling methods with phased data. Numerical examples in two dimensions are also presented to demonstrate their feasibility and effectiveness.

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Section: Introductionmentioning

confidence: 99%

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Liu

Zhang

2019

Journal of Computational Physics: X

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“…A survey on the state of the art of the RLM can be found in [3]. There are also many direct methods without using direct solvers, see e.g., the MUSIC algorithm [14] for locating small inhomogeneities, the Fourier method [40], the multi-frequency factorization method [15], and the direct sampling method [1] for source reconstructions, the multi-frequency linear sampling method [16], the eigenvalue method [39] and an eigenfunction based scheme [32] for obstacle reconstructions.…”

Section: Introductionmentioning

confidence: 99%

“…Both the point like scatterers and the extended scatterers are considered. Our method is motivated by a recent work [1], where a direct sampling method for source support reconstruction is proposed. The key observation for the source problem is that the far field measurement is just the Fourier transform of the unknown source term.…”

Section: Introductionmentioning

confidence: 99%

Inverse acoustic scattering problems with multi-frequency sparse backscattering far field data

Ji,

Liu

2019

Preprint

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The inverse acoustic obstacle problems using multi-frequency backscattering far field patterns at isolated directions are studied. The obstacle could be sound soft or sound hard. We show that the smallest strip containing the obstacle can be uniquely determined by the backscattering far field patterns for all frequencies in a bounded interval at two observation directions. Thus, a support of the obstacle can be determined with multi-frequency far field patterns at 2n observation directions. Here, n is the spatial dimension. The key ingredients are the Kirchhoff approximation and the Fourier transform. Some direct sampling methods using a few multi-frequency backscattering far field patterns are then proposed to reconstruct the obstacle. An important feature of these direct sampling methods is that the indicators are computed only at the sampling points on a line parallel to the observation direction. With the increase of the observation directions, the location and shape can be well captured, even the obstacle has concave part or multiple multi-scalar components. The point like scatterers are also considered. We show that the multi-frequency backscattering far field patterns at a single observation direction are enough to determining the hyper planes containing the point like scatterers. The indicators used for extended obstacles are also applicable for point like scatterers. As an extension, a novel direct sampling method is proposed for phaseless inverse problem with sparse phaseless backscattering data. Numerical examples in two dimensions are presented to validity the effectiveness and robustness of the proposed direct sampling methods.

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“…The conditional stability estimate of the wave equation on a line related to the inverse source problem is provided by [11,12]. The reconstruction of acoustic sources using multiple frequency data of one observation point is analyzed in [3], and a variety of multi-frequency inverse source problems are carefully analyzed in [7,8,27,39]. Analysis of random sources can be seen in [5,26].…”

Section: Introductionmentioning

confidence: 99%

Numerical schemes to reconstruct three dimensional time-dependent point sources of acoustic waves

Chen,

Guo,

et al. 2019

Preprint

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This paper is concerned with the numerical simulation of the three dimensional time-dependent inverse source problem of acoustic waves. The modified method of fundamental solutions (MMFS), which expands the solution utilizing the time convolution of the Green's function and the signal function, are proposed to reconstruct both multiple stationary point sources and a moving point source. For the reconstruction of a moving point source, moreover, the MMFS is simplified as a simple sampling method at each time steps. Numerical experiments are provided to show the effectiveness of the proposed methods.

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Fast acoustic source imaging using multi-frequency sparse data

Cited by 10 publications

References 1 publication

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Inverse acoustic scattering problems with multi-frequency sparse backscattering far field data

Numerical schemes to reconstruct three dimensional time-dependent point sources of acoustic waves

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