Dynamic magnetic resonance elastography can visualize and measure propagating shear waves in tissue-like materials subjected to harmonic mechanical excitation. This allows the calculation of local values of material parameters such as shear modulus and attenuation. Various inversion algorithms to perform such calculations have been proposed, but they are sensitive to areas of low displacement amplitude (and hence low SNR) that result from interference patterns due to reflection and refraction. A spatio-temporal directional filter applied as a pre-processing step can separate interfering waves so they can be processed separately. Weighted combinations of inversions from such directionally separated data sets can significantly improve reconstructions of shear modulus and attenuation.