We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.
Scopus Subject Areas
- Applied Mathematics
- Electroencephalography and magnetoencephalography
- Identifiability and uniqueness
- Inverse boundary problem
- Maxwell system