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Cardiac motion estimation is an important diagnostic tool for detecting heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate cardiac motion using ultrafast ultrasound data. Our solution is based on a variational formulation characterized by the L 2 -regularized class. Displacement is represented by a lattice of b-splines and we ensure robustness, in the sense of eliminating outliers, by applying a maximum likelihood type estimator. While this is an important part of our solution, the main object of this work is to combine low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows one to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. The low-rank constraint speeds up the convergence of the optimization problem while topology preservation ensures a more accurate displacement. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that exhibit motion.

Estimation of the cardiac motion is very important in order to detect heart diseases. This work presents a cardiac motion estimation approach using ultrafast ultrasound data. We optimize a variational framework which has the benefits of combining low-rank data representation with topology preservation. We show through the analysis of experimental results that this combination offers a radical reduction in computational time and noise while ensuring preservation of the anatomical structure of the heart under complex deformations. Although in this work we use the heart as a study case, our solution is promising to analyze other organs experiencing motion.