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Stability and reconstruction of a special type of anisotropic conductivity in magneto-acoustic tomography with magnetic induction

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.