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Cardiac motion estimation is an important diagnostic tool to detect heartdiseases and it has been explored with modalities such as MRI and conventionalultrasound (US) sequences. US cardiac motion estimation still presentschallenges because of the complex motion patterns and the presence of noise. Inthis work, we propose a novel approach to estimate the cardiac motion usingultrafast ultrasound data. -- Our solution is based on a variationalformulation characterized by the L2-regularized class. The displacement isrepresented by a lattice of b-splines and we ensure robustness by applying amaximum likelihood type estimator. While this is an important part of oursolution, the main highlight of this paper is to combine a low-rank datarepresentation with topology preservation. Low-rank data representation(achieved by finding the k-dominant singular values of a Casorati Matrixarranged from the data sequence) speeds up the global solution and achievesnoise reduction. On the other hand, topology preservation (achieved bymonitoring the Jacobian determinant) allows to radically rule out distortionswhile carefully controlling the size of allowed expansions and contractions.Our variational approach is carried out on a realistic dataset as well as on asimulated one. We demonstrate how our proposed variational solution deals withcomplex deformations through careful numerical experiments. While maintainingthe accuracy of the solution, the low-rank preprocessing is shown to speed upthe convergence of the variational problem. Beyond cardiac motion estimation,our approach is promising for the analysis of other organs that experiencemotion.

Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach