Fast LV motion estimation using subspace approximation techniques.

Cardiac motion estimation is very important in understanding cardiac dynamics and in noninvasive diagnosis of heart disease. Magnetic resonance (MR) imaging tagging is a technique for measuring heart deformations. In cardiac tagged MR images, a set of dark lines are noninvasively encoded within myocardial tissue providing the means for measurement of deformations of the heart. The points along tag lines measured in different frames and in different directions carry important information for determining the three-dimensional nonrigid movement of left ventricle. However, these measurements are sparse and, therefore, multidimensional interpolation techniques are needed to reconstruct a dense displacement field. In this paper, a novel subspace approximation technique is used to accomplish this task. We formulate the displacement estimation as a variational problem and then project the solution into spline subspaces. Efficient numerical methods are derived by taking advantages of B-spline properties. The proposed technique significantly improves our previous results reported in [3] with respect to computational time. The method is applied to a temporal sequence of two-dimensional images and is validated with simulated and in vivo heart data.