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 domain³ 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 (.)=A(.,(.)) inΏ, where [¹,]A(.,t) is a one-parameter family of matrixvalued functions which are a priori known to be C1, allowing us to stably reconstruct in Ώin terms of an internal functional F(). Our results also extend previous results in MAT-MI where(.) =(.)D(.), with D an a priori known matrix-valued function on Ώto a more general anisotropic structure which depends nonlinearly on the scalar function to be reconstructed.