On an inverse boundary problem arising in brain imaging

TL;DR

This paper addresses an inverse boundary problem in brain imaging, demonstrating conditions under which both the electric current source and electromagnetic parameters can be uniquely recovered from boundary data.

Contribution

It establishes the recoverability of sources and parameters in brain imaging models under specific invariance and piecewise constant assumptions.

Findings

Unique recovery of source and parameters under invariance conditions

Recovery possible when parameters are piecewise constant

Applicable to models with boundary measurements in brain imaging

Abstract

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 current source is invariant in a fixed direction or a harmonic function.