Velocity estimation with 3D spatiotemporal filtering of sequences of ultrasound images: A Fourier approach

Blood velocity estimation is required in many clinical applications. Ultrasonic imaging is often used to reach this goal. This article presents a velocity vector estimation method from ultrasonic imaging. It complements Doppler imaging, which has several limitations. Our method is based on spatiotemporal filtering to estimate the apparent velocity vector for each pixel of the sequence of B-mode imaging. Jacobson [1] then Porat [2] showed that the three-dimensional Fourier transform of a sequence in translation is zero except for a plane plane passing through the origin. The slope of this plane is proportional to the velocity components ν_x and ν_y. We suggest to design a bank of filters in order to estimate this slope then deduce the velocity vector. The method was applied to sequences of ultrasound images of calibrated flow in a vessel (mean velocity <; 1 mm/s). The velocity estimates obtained are exhibited mean errors inferior to 9%. Results are presented as dynamic cartography and dense fields of velocity vectors. Associated velocity profiles show good agreement with the theoretical parabolic profile of laminar flow.