Visualizing action potentials within the cardiac tissue enables the identification of abnormal action potential wave propagation patterns for use in both clinical and cardiac research settings. Otani et al. have been investigating the possibility of using 4-D (three spatial dimensions and one time dimension) mechanical deformation data, obtained either from MRI or ultrasound images to reverse-calculate these action potential patterns. However, the inverse system is extremely sensitive to noise; that is, a small amount of perturbation from the signal can lead to a substantial perturbation in the solution if the perturbation has a high-frequency component. Here, we explore three noise reduction methods, in an attempt to reduce the effect of noise in the input data and to regularize the calculated solution.