The standard deviation on the blood velocity estimates are influenced by measurement noise, velocity spread, and signal alteration introduced by de-noising and clutter filters. A noisy and non-smooth appearance of the velocity distribution is obtained, which is not consistent with the actual velocity in the vessels. Post-processing is beneficial to obtain an image that minimizes the variation, and present the important information to the clinicians. Applying the theory of fluid mechanics introduces restrictions on the variations possible in a flow field. Neighboring estimates in time and space should be highly correlated, since transitions should occur smoothly. This idea is the basis of the algorithm developed in this study. From Bayesian image processing theory an a posteriori probability distribution for the velocity field is computed based on constraints on smoothness. An estimate of the velocity in a given point is computed by maximization of the probability, given prior knowledge of the original estimate in that position, and the estimates in the neighboring positions in time and space. The method has been tested on simulated 2D RF-data resembling signals from the carotid artery with different signal-to-noise ratios (SNR). The exact extent of the vessel and the true velocities are thereby known. Velocity estimates were obtained by employing Kasai's autocorrelator on the data. The post-processing filter was used on the computed 2D velocity map. An improvement of the RMS error in the range of 15-53% was observed. For low SNRs the highest improvement was obtained. Visual inspection of the images show a high qualitative improvement. A more smooth profile has been obtained, which more closely resembles the true smooth profile. The same conclusion can be drawn after application of the filter to in-vivo data acquired with a dedicated sampling system.
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