A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

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 the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with 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, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data.

References in corpus (3)

• A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
• 2D and 3D reconstructions in acousto-electric tomography
• Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries

Cited by in corpus (4)

• Photoacoustic Tomography in a Rectangular Reflecting Cavity
• Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data
• Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography
• New Stability Estimates for the Inverse Medium Problem with Internal Data