This paper describes the mathematical grounds for a highly undersampled magnetic resonance electrical impedance tomography (MREIT) method, with the aim of visualizing the dynamic changes in electrical tissue properties that occur in response to physiological activity. MREIT with fully sampled magnetic resonance (MR) data (satisfying the Nyquist criterion) has been shown to be capable of high-resolution conductivity imaging in numerical simulations and in animal experiments. However, when the data are undersampled (violating the Nyquist criterion for reducing data acquisition time), it is difficult to extract the component of magnetic flux density that is induced by boundary injection currents, and it is the data from this component that are used in performing the standard MREIT algorithm. Here, we show that it is possible to localize small conductivity perturbations using highly undersampled MR data. We perform various numerical simulations to support our theoretical results.
All Science Journal Classification (ASJC) codes
- Applied Mathematics