Determining both sound speed and internal source in thermo- and photo-acoustic tomography

Liu, Hongyu; Uhlmann, Günther

doi:10.1088/0266-5611/31/10/105005

Cited by 100 publications

(102 citation statements)

References 13 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…Finally, we briefly discuss the mathematical arguments and technical novelties for the current study. Our mathematical techniques are inspired by [14] mentioned earlier by one of the authors of this article for the simultaneous recovery in theormoacoustic and photoacoustic tomography. In [14], the lowfrequency asymptotics of the wave fields is used to extract the information of the sound speed and the internal source, respectively.…”

Section: )mentioning

confidence: 99%

Determining a fractional Helmholtz equation with unknown source and scattering potential

Cao

Liu

2019

Communications in Mathematical Sciences

Self Cite

View full text Add to dashboard Cite

We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequencydependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo-and photo-acoustic tomography.

show abstract

Section: )mentioning

confidence: 99%

Determining a fractional Helmholtz equation with unknown source and scattering potential

Cao

Liu

2019

Communications in Mathematical Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The problems of locating or imaging the source excitations using wave propagation make enormous demands on a wide range of realistic engineering applications. Typical scenarios of such inverse source problems include acoustic tomography [5,18,19] and medical imaging [2,4,6,11,13]. In the last decades, great efforts had been devoted to the numerical methods for the inverse source problem of determining an acoustic source.…”

Section: Introductionmentioning

confidence: 99%

Retrieval of acoustic sources from multi-frequency phaseless data

Zhang

Guo

et al. 2018

Inverse Problems

Self Cite

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

“…This problem has been investigated by several authors in recent years, for example in [4,5,6,16,26]. It has a wide range of applications, for example in optical tomography [3], antenna control [18] and in the acoustic reconstruction part of several hybrid imaging methods, most notably photo-and thermoacoustic tomography [2,19], see also [1,6]. The single-frequency ISP, i.e., when one only has a measurement at a single frequency, is not uniquely solvable due to F k having a large kernel.…”

Section: Introductionmentioning

confidence: 99%

Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem

2018

View full text Add to dashboard Cite

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the source. We study the problem in a certain finite dimensional setting: From measurements made at a finite set of frequencies we uniquely determine and reconstruct sources in a subspace spanned by finitely many Fourier-Bessel functions. Further, we obtain a constructive criterion for identifying a minimal set of measurement frequencies sufficient for reconstruction, and under an additional, mild assumption, the reconstruction method is shown to be stable. Our analysis is based on a singular value decomposition of the source-to-measurement forward operators and the distribution of positive zeros of the Bessel functions of the first kind. The reconstruction method is implemented numerically and our theoretical findings are supported by numerical experiments. arXiv:1803.05010v1 [math.NA]

show abstract

Determining both sound speed and internal source in thermo- and photo-acoustic tomography

Cited by 100 publications

References 13 publications

Determining a fractional Helmholtz equation with unknown source and scattering potential

Determining a fractional Helmholtz equation with unknown source and scattering potential

Retrieval of acoustic sources from multi-frequency phaseless data

Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem

Contact Info

Product

Resources

About