Nguyen, L., & Kunyansky, L. (2016). A dissipative time reversal technique for photo-acoustic tomography in а cavity. SIAM J. Imaging Science, 9(2), 748–769.
Kunyansky, L. (2012). A mathematical model and inversion procedure for magneto-acousto-electric tomography. Inverse Problems, 28(3).
Abstract:
Magneto-acousto-electric tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable electrical impedance tomography. In this paper, we analyze the existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with the MAET. It consists in applying to the data one of the algorithms of thermo-acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, the MAET is a stable technique yielding high-resolution images even in the presence of significant noise in the data. © 2012 IOP Publishing Ltd.
