Modified forward and inverse Born series for the Calderon and diffuse-wave problems

Abhishek, Anuj; Bonnet, Marc; Moskow, Shari

doi:10.1088/1361-6420/abae11

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…Since the cost function for the inverse problem of determining coefficients of the diffusion equation in (1) has a complicated landscape, the reconstructed value is trapped in a local minimum if iterative schemes such as the Levenberg-Marqusrdt, Gauss-Newton, and conjugate gradient methods are used. An alternative approach is the use of direct methods in which perturbations of coefficients are reconstructed.…”

Section: Introductionmentioning

confidence: 99%

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The inverse Rytov series for diffuse optical tomography

Machida

2023

Inverse Problems

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The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not necessary and higher order terms in the Rytov series can be used for reconstruction. The convergence and stability are discussed. We find that the inverse Rytov series has a recursive structure similar to the inverse Born series.

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Section: Introductionmentioning

confidence: 99%

“…The inverse Born series was extended to Banach spaces [4,16]. Recently, a modified Born series with unconditional convergence was proposed and its inverse series was studied [1]. The convergence theorem for the inverse Born series has recently been improved [11].…”

Section: Introductionmentioning

confidence: 99%

The inverse Rytov series for diffuse optical tomography

Machida

2023

Inverse Problems

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“…The inverse Born series was extended to Banach spaces [4,15]. Recently, a modified Born series with unconditional convergence was proposed and its inverse series was studied [1]. The convergence theorem for the inverse Born series has recently been improved [10].…”

Section: Introductionmentioning

confidence: 99%

The inverse Rytov series for diffuse optical tomography

Machida¹

2022

Preprint

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The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography.In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not necessary and higher order terms in the Rytov series can be used for reconstruction. The convergence and stability are discussed. We find that the inverse Rytov series has a recursive structure similar to the inverse Born series.

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“…Jakobsen and Wu (2016) have replaced the Born series with a convergent renormalized scattering series by utilizing the leading De Wolf approximation. By using the modified volume integral equation proposed by Bonnet and others (2017), Abhishek et al (2020) have developed a modified Born series, that is unconditionally convergent, for the forward and inverse scattering problem.…”

Section: Introductionmentioning

confidence: 99%

“…By using the modified volume integral equation proposed by Bonnet and others (2017), Abhishek et al . (2020) have developed a modified Born series, that is unconditionally convergent, for the forward and inverse scattering problem.…”

Section: Introductionmentioning

confidence: 99%

Homotopy scattering series for seismic forward modelling with variable density and velocity

Xiang

Eikrem

Jakobsen

et al. 2021

Geophysical Prospecting

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We have derived a convergent scattering series solution for the frequency-domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann-Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann-Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann-Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like N 3 , where N is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann-Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so-called homotopy analysis method to derive an iterative solution for the vectorial Lippmann-Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as N 2 . Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three-layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.

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Modified forward and inverse Born series for the Calderon and diffuse-wave problems

Cited by 5 publications

References 21 publications

The inverse Rytov series for diffuse optical tomography

The inverse Rytov series for diffuse optical tomography

The inverse Rytov series for diffuse optical tomography

Homotopy scattering series for seismic forward modelling with variable density and velocity

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