Statistical analysis of decorrelation-based transducer tracking for three-dimensional ultrasound

The use of speckle decorrelation techniques to calculate the displacement of a moving transducer has shown promise. We describe a technique to estimate displacement between pairs of parallel planes without assuming that plane separation in the scan is uniform. We perform theoretical and empirical analyses of the bias and uncertainty in plane spacing estimates as a function of speckle size, patch size, and the number of planes used for normalization. Practically, only the central, linear region of the autocovariance curves can be used in this decorrelation method, which implies that distance between acquired image planes should be approximately half the speckle size. In this region, the uncertainty in estimated plane spacing was less than 15% for a 8.1 mm (axial) by 9.1 mm (lateral) patch and increased to 33% for an 8.1 mm (axial) by 1.5 mm (lateral) patch. The number of planes, Nz, used to calculate the normalization factors (averages of brightness and- squared brightness) was a major source of bias. Optimum Nz was found to be five to ten planes, depending on distance between acquired image planes, with a poor choice of Nz resulting in a bias of 10% or greater. A second source of bias is brightness gradients which, although they appear very slight on intensity images, can cause a large bias is the plane spacing estimates made using linearized data.