  This paper addresses the challenging task of guide wire navigation in
cardiovascular interventions, focusing on the parameter estimation of a guide
wire system using Ensemble Kalman Inversion (EKI) with a subsampling technique.
The EKI uses an ensemble of particles to estimate the unknown quantities.
However since the data misfit has to be computed for each particle in each
iteration, the EKI may become computationally infeasible in the case of
high-dimensional data, e.g. high-resolution images. This issue can been
addressed by randomised algorithms that utilize only a random subset of the
data in each iteration. We introduce and analyse a subsampling technique for
the EKI, which is based on a continuous-time representation of stochastic
gradient methods and apply it to on the parameter estimation of our guide wire
system. Numerical experiments with real data from a simplified test setting
demonstrate the potential of the method.
