Extensive air showers developing through the atmosphere emit radio signals, which can be measured by antennas on ground. Multiple antennas measure this radio footprint as voltage signals as a function of time. Information Field Theory (IFT) is a framework to address field reconstruction problems with many degrees of freedom, such as imaging, and is based on Bayesian statistics. With IFT, it is possible to approximate posterior distributions over field configuration spaces and thereby to effectively invert measurements. An inference process based on IFT is devised to reconstruct the four-dimensional distribution of currents in the atmosphere. Inside a volume along to the shower axis, is filled with non-parametric structures describing the mascroscopic currents that would produce the electric field at the antennas. In this contribution, we demonstrate this approach on a toy example to investigate technical limitations and challenges.