Cardiac motion estimation from ultrasound images is an ill-posed problem that needs regularization to stabilize the solution. In this work, regularization is achieved by exploiting the sparseness of cardiac motion fields when decomposed in an appropriate dictionary, as well as their smoothness through a classical total variation term. The main contribution of this work is to robustify the sparse coding step in order to handle anomalies, i.e., motion patterns that significantly deviate from the expected model. The proposed approach uses an ADMM-based optimization algorithm in order to simultaneously recover the sparse representations and the outlier components. It is evaluated using two realistic simulated datasets with available ground-truth, containing native outliers and corrupted by synthetic attenuation and clutter artefacts.