Sensorless freehand 3-D ultrasound using regression of the echo intensity

In freehand 3-D ultrasound (US), a position sensor is attached to the probe of a 2-D US machine. The resulting 3-D data permit flexible visualisation and more accurate volume measurement than can be achieved using 2-D B-scans alone; however, the use of the position sensor can be inconvenient for the clinician. The objective is, thus, to replace the sensor with a technique for estimating the probe trajectory based on the B-scan images, themselves. One such technique exists, based on decorrelation algorithms. This paper presents an alternative approach based on linear regression of the echo-envelope intensity signal. A probabilistic analysis of the speckle characteristics of the US signal leads to a linear model, on which the regression algorithm is based. The gradient parameter of this model is shown to be directly related to probe motion. The viability of the new approach is demonstrated through simulations and in vitro and in vivo experiments.