Regularized, weighted temporal multiresolution speckle tracking of small displacements in ultrasound

A new referencing scheme for estimating axial displacements with ultrasound is presented. The multiresolution scheme combines estimates made at multiple temporal spacings into a single, noise robust, high resolution estimate. The problem is framed as an overdetermined system of equations, and the least-squares solution is solved directly. Weighting of input estimates allows for automatic rejection of decorrelated data, and Tikhonov regularization enforces smoothness constraints. This scheme is particularly useful for estimating motion with decorrelated frames, such as with Acoustic Radiation Force Impulse (ARFI) imaging.