Magnetic field tomography was applied to reconstruct the oscillating interface between liquid GaInSn alloy and aqueous KOH solution in a simplified cylindrical aluminum reduction cell. A direct electric current was imposed similar to the industrial reduction procedure, and a pneumatic shaker was used to excite interfacial instabilities with non-axisymmetric interface modes at the same time. The deformed interface led to a perturbation to the magnetic field which was measured by a sensor array. By fast Fourier Transforms, a database was generated and exploited to reconstruct the interface oscillation by solving an inverse problem.