Magneto-Acousto-Electric Tomography with Magnetic Field Measurements: Modeling, Inversion and Stability

Magneto-acousto-electric tomography (MAET) combines ultrasound with a static magnetic field to infer the electrical conductivity of an object. In this paper, we present a rigorous quasi-static mathematical model for MAET with magnetic field measurements and introduce an adjoint problem to decouple the resulting hybrid inverse problem. This yields a two-step inversion procedure: solving an acoustic inverse source problem and then recovering the conductivity from an internal current density. For the second step, by exploiting the analytic structure of a coil-determined field, we establish an interior Hölder stability estimate without imposing a pointwise nonzero constraint on the internal data. We further prove that, under explicit smallness assumptions on the conductivity and coil geometry, the conductivity can be recovered with region-of-interest Lipschitz stability in both bounded and half-space geometries.