An Acousto-electric Inverse Source Problem

Wei, Li; Schotland, John C.; Yang, Yang; Zhong, Yimin

doi:10.1137/21m1406568

Cited by 4 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This question arises in Acousto-Electric Tomography that aims at reconstructing the unknown interior conductivity σ from internal data composed of power density measurements [ZW04,Amm+08]. Similar questions appear in other imaging methods including Current Density Imaging [WS12, Bal13,Li+21] and Magnetic Resonance Electric Impedance Tomography [SKW05,SW11] that aim at reconstructing the conductivity from current density measurements. These questions are relevant in any dimension n ⩾ 2, but in this article, we will restrict our attention only on the two-dimensional case.…”

Section: Introductionmentioning

confidence: 90%

Jacobian of solutions to the conductivity equation in limited view

Salo¹,

Schlüter²

2022

Inverse Problems

View full text Add to dashboard Cite

The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the boundary functions so that the Jacobian of the corresponding solutions is non-vanishing. In that regard we allow for discontinuous boundary functions, which requires the use of solutions in weighted Sobolev spaces. We implement the procedure of reconstructing a conductivity from power density data numerically and investigate how this limited view setting affects the Jacobian and the quality of the reconstructions.

show abstract

Section: Introductionmentioning

confidence: 90%

Jacobian of solutions to the conductivity equation in limited view

Salo¹,

Schlüter²

2022

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…This fact helps us to design suitable boundary conditions and thereby prove a Lipschitz stability for (IP). Stability of acousto-electric tomography (AET) [21] and an acousto-electric inverse source problem [22] have been proved based on this observation. For more applications of CGO solutions to coupled physics inverse problems, see [23] and the references therein.…”

Section: Introductionmentioning

confidence: 91%

Lipschitz stability of recovering the conductivity from internal current densities

Qiu

Zheng

2023

Inverse Problems

View full text Add to dashboard Cite

In recent years, coupled physics imaging techniques have been developed to produce clearer images than those produced by electrical impedance tomography. This paper focuses on the inverse problem arising in current density impedance imaging and magneto-acousto-electric tomography.  We consider the electrostatic equation $\nabla\cdot(\sigma\nabla w_b) = 0$ in a bounded domain $\Omega\subset\mathbb{R}^3$ with either the Dirichlet or Neumann boundary condition $b$, where $\sigma$ is a scalar conductivity function. The inverse problem is formulated as recovering $\sigma$ from vector fields $J_b = \sigma\nabla w_b$ with different boundary conditions $b$.  We provide a local Lipschitz stability, stating that near some known $\sigma_0$ and under some regularity assumptions, we can find $b_1$ and $b_2$ by constructing complex geometrical optics (CGO) solutions such that $\|\ln\sigma^{(1)} - \ln\sigma^{(2)}\|_{C^{m,\alpha}(\overline{\Omega})} \le C\sum_{j=1}^2 \|J_{b_j}^{(1)} - J_{b_j}^{(2)}\|_{C^{m,\alpha}(\overline{\Omega})}$.  Furthermore, we modify the CGO solutions using the reflection method to make $b_1$ and $b_2$ vanish on a portion of a plane, and prove a local Lipschitz stability with partial data.

show abstract

“…We begin by developing a simple model for acoustic modulation of the electrical current density and material parameters, following the approach of [26]. We begin by considering the time-harmonic Maxwell equations in a bounded domain Ω ⊂ R 3 :…”

Section: Modelmentioning

confidence: 99%

“…We now examine the effect of acoustic modulation. Following [6,26], we consider a system of charge carriers in a fluid, in which a small-amplitude acoustic plane wave propagates. It follows that the current density J δ is modulated according to…”

Section: Modelmentioning

confidence: 99%

“…In this paper, we propose an alternative approach to the electromagnetic inverse source problem. In this approach, which is an extension of the authors' previous work on the acousto-electric inverse source problem for static fields [26], a wavefield is used to control the material properties of a medium of interest, which is then probed by a second wavefield. Also see related work on hybrid imaging [2-7, 10, 12-15, 19, 22-26, 28, 31, 32].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation