Levenberg–Marquardt Algorithm for Acousto-Electric Tomography based on the Complete Electrode Model

Li, Changyou; Karamehmedović, Mirza; Sherina, Ekaterina; Knudsen, Kim

doi:10.1007/s10851-020-01006-y

Cited by 8 publications

(4 citation statements)

References 29 publications

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“…AET was considered experimentally in [33], however, since the measurements have very low signal-to-noise ratio, the technology is still in its infancy and many technological challenges need to be solved. Mathematically, the problem is fairly well understood [5,7,8,10,21,22,27] and several numerical algorithms have been discussed [2,3,6,17,24,31]. For an introduction to the mathematical theory pertaining to both AET and related problems we refer to the book [4].…”

Section: Introductionmentioning

confidence: 99%

Sound speed uncertainty in acousto-electric tomography

Jensen¹,

Knudsen²

2021

Inverse Problems

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The goal in acousto-electric tomography is to reconstruct an image of the unknown electric conductivity inside an object from boundary measurements of electrostatic currents and voltages collected while the object is penetrated by propagating ultrasound waves. This problem is a coupled-physics inverse problem. Accurate knowledge of the propagating ultrasound wave is usually assumed and required, but in practice tracking the propagating wave is hard due to inexact knowledge of the interior acoustic properties of the object. In this work, we model uncertainty in the sound speed of the acoustic wave, and formulate a suitable reconstruction method for the interior power density and conductivity. We also establish theoretical error bounds, and show that the suggested approach can be understood as a regularization strategy for the inverse problem. Finally, we numerically simulate the sound speed variations from a numerical breast tissue model, and computationally explore the effect of using an inaccurate sound speed on the error in reconstructions. Our results show that with reasonable uncertainty in the sound speed reliable reconstruction is still possible.

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Section: Introductionmentioning

confidence: 99%

Sound speed uncertainty in acousto-electric tomography

Jensen¹,

Knudsen²

2021

Inverse Problems

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“…Most commonly, the reconstruction problem in EIT is formulated in a variational setting and solved by iterative methods that minimize the error between measured voltages V and simulated voltages U (σ) corresponding to a guess conductivity σ. Additional regularization is needed due to the ill-posedness and instability of the reconstruction problem; popular approaches include the Levenberg-Marquardt (LM) algorithm [16], Tikhonov regularization [17], and Total Variation (TV) regularization [18]. These methods frequently suffer from high sensitivity to modeling errors and, if not compensated for, are limited in practice to time-difference EIT imaging which recovers the change in conductivity ∆σ relative to a reference data set/frame.…”

Section: Case Study: Electrical Impedancementioning

confidence: 99%

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Herzberg

Rowe

Hauptmann

et al. 2021

IEEE Trans. Comput. Imaging

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The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has strong generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

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“…Several different linearization methods were compared in [21] giving rise to the analysis of artifacts in [6]. A numerical reconstruction method based on the Levenberg-Marquardt iteration was developed in [7,34] and methods using an explicit least squares optimization approach are found in [1,2,33,42]; the limited angle problem was considered in [23,24]. See also, e.g.…”

Section: Introductionmentioning

confidence: 99%

Feasibility of acousto-electric tomography

Jensen,

Kirkeby,

Knudsen

2024

Inverse Problems

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In acousto-electric tomography (AET) the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is perturbed by a time-dependent acoustic wave, thus taking advantage of the acousto-electric effect. We approach the AET reconstruction in two steps: First, the interior power density is obtained from boundary measurements by solving a linear inverse and ill-posed problem; second, the interior conductivity is reconstructed from the power density by solving a non-linear and well-posed problem. Mathematically these inverse problems are fairly well understood, and reconstruction methods work well on synthetic data. This is in contrast to experimental findings. An effect can indeed be observed and data can be collected. However, the acousto-electric coupling is very weak, and consequently, the change in the measured voltage due to the acoustic perturbation might be too small compared to the background noise for viable reconstructions. In this paper, we take one step towards understanding the feasibility of AET. We provide an in-silico model of the coupled physics scenario based on standard models for the individual phenomena. Moreover, we formulate and implement numerically a full reconstruction method for the inverse problem via the two steps. We perform computational experiments with realistically chosen parameters from the context of medical imaging. The focus is on understanding the role of the acousto-electric coupling parameter and the signal-to-noise ratio (SNR). The critical signal strength is analyzed and the omnipresent Johnson-Nyquist noise is estimated. We obtain both positive and negative findings; we can reconstruct features even under severe noise conditions, but we also find that the SNR one is likely to face in practice is too low to obtain useful reconstructions.

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Levenberg–Marquardt Algorithm for Acousto-Electric Tomography based on the Complete Electrode Model

Cited by 8 publications

References 29 publications

Sound speed uncertainty in acousto-electric tomography

Sound speed uncertainty in acousto-electric tomography

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Feasibility of acousto-electric tomography

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