Stroke is a leading cause of death all around the world. There are two main types of stroke:
ischemic (blood clot preventing blood flow to a part of the brain) and hemorrhagic (bleeding in
the brain). The symptoms are the same, but treatments very different. A portable “stroke
classifier” would be a life-saving equipment to have in ambulances, but so far it does not exist.
Electrical Impedance Tomography (EIT) is a promising and harmless imaging method for stroke
classification. In EIT one attempts to recover the electric conductivity inside a domain from
electric boundary measurements. This is a nonlinear and ill-posed inverse problem. The so-called
Complex Geometric Optics (CGO) solutions have proven to be a useful computational tool for
reconstruction tasks in EIT . A new property of CGO solutions is presented, showing that a one-dimensional Fourier transform in the spectral variable provides a connection to parallel-beam Xray tomography of the conductivity. One of the consequences of this “nonlinear Fourier slice theorem” is a novel capability to recover inclusions within inclusions in EIT . In practical imaging, measurement noise causes strong blurring in the recovered profile functions. However, machine learning algorithms can be combined with the nonlinear PDE techniques in a fruitful way. As an
example, simulated strokes are classified into hemorrhagic and ischemic using EIT measurements.