Lagrangian speckle model and tissue-motion estimation - Theory

It is known that when a tissue is subjected to movements such as rotation, shearing, scaling, etc., changes in speckle patterns that result act as a n oise source, often responsible for most of the displacement-estimate varian ce. From a modeling point of view, these changes can be thought of as resul ting from two mechanisms: one is the motion of the speckles and the other, the alterations of their morphology. In this paper, we propose a new tissue -motion estimator to counteract these speckle decorrelation effects. The es timator is based on a Lagrangian description of the speckle motion. This de scription allows us to follow local characteristics of the speckle field as if they were a material property. This method leads to an analytical descr iption of the decorrelation in a way which enables the derivation of an app ropriate inverse filter for speckle restoration. The filter is appropriate for linear geometrical transformation of the scattering function (LT), i.e. , a constant-strain region of interest (ROI). As the LT itself is a paramet er of the filter, a tissue-motion estimator can be formulated as a nonlinea r minimization problem, seeking the best match between the pre-tissue-motio n image and a restored-speckle post-motion image. The method is tested, usi ng simulated radio-frequency (RF) images of tissue undergoing axial shear.