KEYWORDS: Blood, Ultrasonography, Signal to noise ratio, Transducers, Doppler effect, Blood circulation, Speckle, Monte Carlo methods, Scanners, Tissues
Most modern ultrasound scanners use the so-called pulsed-wave
Doppler technique to estimate the blood velocities. Among the
narrowband-based methods, the autocorrelation estimator and the
Fourier-based method are the most commonly used approaches. Due to
the low level of the blood echo, the signal-to-noise ratio is low,
and some averaging in depth is applied to improve the estimate.
Further, due to velocity gradients in space and time, the spectrum
may get smeared. An alternative approach is to use a pulse
with multiple frequency carriers, and do some form of averaging in
the frequency domain. However, the limited transducer bandwidth
will limit the accuracy of the conventional Fourier-based
estimator; this method is also known to have considerable
variance. More importantly, both the mentioned methods suffer from
the maximum axial velocity bound, vzmax = cfprf/4fc, where c is the speed of propagation. In this paper, we propose a nonlinear least squares (NLS) estimator. Typically, NLS estimators are computationally cumbersome, in general requiring the minimization of a multidimensional and often multimodal cost function. Here, by noting that the unknown velocity will result in a common known frequency distorting function, we reformulate the NLS estimator as an one-dimensional minimization problem confirmed by extensive simulations. The results show that the NLS method not only works better than both the autocorrelation estimator and Periodogram method for high velocities, it will also not suffer from the maximum velocity
bound.
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