Fast computation of tagged MRI motion fields with subspace approximation techniques

MRI tagging is a technique for measuring heart deformations. In tagged MR images, a set of dark lines are encoded within the deforming Left-Ventricle (LV) tissue for quantitative measurement of motion. The points along tag lines measured at different frames and different directions carry important information for measuring the 3D motion of LV. However, these measurements are sparse and therefore multidimensional interpolation techniques are needed to reconstruct a dense displacement field. Here, a novel spline technique is used to accomplish this task. The authors formulate the displacement estimation as a variational problem and then use B-spline bases to approximate the solution. Efficient numerical methods are derived by taking advantages of B-spline properties. The proposed techniques can improve the results significantly with respect to computational time as well as the computational accuracy. The new methods have been validated on both simulated and in-vivo heart data