The volume-surface integral equation (VSIE) method is used for rapid and accurate simulations of electromagnetic fields in magnetic resonance imaging. For the case of a 7T array and a numerical head phantom, we constructed the VSIE coupling matrix that models the interactions between the coil and the scatterer. We reshaped the columns of the matrix as incomplete 3D tensors. We investigated how the low rank properties of these tensors, could be exploited to compress the coupling matrix, by expressing the tensors in their canonical form. We showed that an excellent compression could be achieved with an error lower than 2%.