Modeling of the correlation of analytic ultrasound radiofrequency signals for angle-independent motion detection

Conventional pulsed ultrasound systems are able to assess motion of scatterers in the direction of the ultrasound beam, i.e., axial motion, by determining the lag at which the maximum correlation occurs between consecutively-received radiofrequency (rf) signals. The accuracy, resolution, and processing time of this technique is improved by making use of a model for the correlation of rf signals. All previously-described correlation models only include axial motion, but it is common knowledge that lateral motion, i.e., motion in the plane perpendicular to the beam axis, reduces the correlation of rf signals in time. In the present paper, a model for the correlation of analytic rf signals in depth and time is derived and verified. It also includes, aside of some signal and transducer parameters, both axial and lateral motion. The influence of lateral motion on the correlation of (analytic) rf signals is strongly related to local phase and amplitude characteristics of the ultrasound beam. It is shown how the correlation model, making use of an ultrasound transducer with a circular beam shape, can be applied to estimate, independent of angle, the magnitude of the actual motion. Furthermore, it is shown that the model can be applied to estimate the local signal-to-noise ratio and rf bandwidth.