Efficacy of Kriging Interpolation in Ultrasound Imaging; Subsample Displacement Estimation

Ultrasound images have an inherently low lateral resolution due to the size of transducers that are used in standard clinical scanners. This makes for low resolution images, as well as imprecise lateral displacement estimation. In speckle tracking, the well known discipline of estimating displacement by tracking pixel movement, lateral interpolation is often used to get subsample accurate displacement estimation. Standard methods for interpolation are known as inverse distance weighting methods, of which the well known cubic interpolation method is a part. Kriging interpolation, however, is a stochastic approach that uses statistical data to calculate interpolated data points as opposed to the purely mathematical methods of more traditional interpolators. This analysis tests the efficacy of one variety of Kriging interpolation, called Simple Kriging, on ultrasound data. Simple Kriging is tested on its accuracy to interpolate a sparse ultrasound image frame, as well as its usefulness in interpolating the correlation map to estimate subsample displacement. The applied bias of the estimation using Simple Kriging is also tested by interpolating the autocorrelation map where displacement is zero. Simple Kriging is an alternative interpolation scheme that could be used with image data and its accuracy is comparable to the accuracy of using the cubic interpolation.