论文标题
具有磁性感应的磁性声学扫描术中特殊类型的各向异性电导率的稳定性和重建
Stability and reconstruction of a special type of anisotropic conductivity in magneto-acoustic tomography with magnetic induction
论文作者
论文摘要
我们通过磁性诱导（MAT-MI）的混合反向问题（MAT-MI），考虑了域中生物组织的稳定性和重建的问题。 The class of anisotropic conductivities considered here is of type $σ(\cdot)=A(\cdot,γ(\cdot))$ in $Ω$, where $[λ^{-1}, λ]\ni t\mapsto A(\cdot, t)$ is a one-parameter family of matrix-valued functions which are \textit{a-priori}已知为$ c^{1，β} $，使我们能够在内部功能$ f（σ）$方面稳定地重建$γ$ $ω$。我们的结果还扩展了MAT-MI的先前结果，其中$σ（\ cdot）=γ（\ cdot）d（\ cdot）$，带有$ d $ an \ textit {a a-priori}已知的矩阵值在$ω$上的$ω$对更普遍的各向异性结构，依赖于scalcor $γ$ reconsction $γ$ reconstonction。
We consider the issues of stability and reconstruction of the electrical anisotropic conductivity of biological tissues in a domain $Ω\subset\mathbb{R}^3$ by means of the hybrid inverse problem of magneto-acoustic tomography with magnetic induction (MAT-MI). The class of anisotropic conductivities considered here is of type $σ(\cdot)=A(\cdot,γ(\cdot))$ in $Ω$, where $[λ^{-1}, λ]\ni t\mapsto A(\cdot, t)$ is a one-parameter family of matrix-valued functions which are \textit{a-priori} known to be $C^{1,β}$, allowing us to stably reconstruct $γ$ in $Ω$ in terms of an internal functional $F(σ)$. Our results also extend previous results in MAT-MI where $σ(\cdot) = γ(\cdot) D(\cdot)$, with $D$ an \textit{a-priori} known matrix-valued function on $Ω$ to a more general anisotropic structure which depends non-linearly on the scalar function $γ$ to be reconstructed.
