A Single Bit RF Domain Complex Cross-Correlation Velocity Estimator for Color Flow Mapping

Abstract

This paper evaluates the performance of a one bit mean frequency estimator to estimate blood flow velocity for ultrasound color flow mapping. This one bit mean frequency estimator, referred to as BC3 estimator, is derived from the recently introduced complex cross-correlation model (C3M) employing the full dynamic data range. The C3M velocity estimator is not suitable for application in color flow mapping because of its high hardware complexity and associated computational load. The BC3 estimator estimates the mean blood flow velocity using only two complex cross-correlation coefficients. For this purpose the latter are computed by means of a complex one bit cross-correlation operation. Each sample of the RF signals is converted into an one bit representation based on the sign of the real and imaginary part of the RF samples. A full derivation and mathematical description of the BC3 estimator is presented. In addition, a thorough performance evaluation of the BC3 estimator in comparison with the full dynamic range C3M velocity estimator is carried out by means of signal simulations to document the effect of signal to noise ratio, sample frequency and bandwidth. For the specific simulation conditions considered the standard deviation of both estimators (C3M and BC3) is comparable. The bias of the BC3 estimator appears to be a function of velocity, while the full dynamic range C3M velocity estimator exhibits no bias. The simulation results are confirmed by evaluation of data from an in vivo measurement. Taking into account the low hardware complexity and computational load in combination with the achieved precision, it may be concluded that the BC3 estimator is well suited for implementation in color flow mapping.