2022/07/29 by Donlon, Niall, Gaburro, Romina, Moskow, Shari +1
#35Q61 #35R30 #65N21 #78A70 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2207.14613
We consider the issues of stability and reconstruction of the electrical anisotropic conductivity of biological tissues in a domain Ω⊂ℝ3 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(⋅)=A(⋅,γ(⋅)) in Ω, where [λ-1, λ]\ni t↦ A(⋅, t) is a one-parameter family of matrix-valued functions which are a-priori known to be C1,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(⋅) = γ(⋅) D(⋅), with D an 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.