Double-stage least-squares regularisation for 3D velocity estimation: a simulation study

The 3D blood velocities estimation using ultrasound imaging is an objective tool for clinical applications (such as cardiac blood flow imaging, etc.), which could be useful in many different situations as it avoids clinicians to mentally reconstruct a volume from a sequence of 2D images. However, it still remains a challenge. To address it, a double-stage leastsquares regularisation method is proposed in this paper based on a transverse oscillation pipeline for the 3D velocity ultrasound estimation of the blood flow. In order to evaluate the accuracy of the proposed method, several simulations are conducted for parabolic flow profiles with maximum velocities ranging from 10 to 50 cm/s considering a synthetic straight vessel phantom. Comparisons of the obtained fields in magnitude and angle are made with a 3D multi-angle cross-beam Doppler (3D-MAD) technique as well as a ground truth velocity. It is seen that the proposed method performs better in average than 3D-MAD for the magnitude, with an improvement of at least 3% relative to the maximum velocity.