The swept scan technique has been employed in high frequency ultrasonic imaging with a mechanically scanned single element transducer. It improves the scanning speed over the discrete scan technique. Although the technique has been widely adopted, effects of continuous scanning on accuracy of blood flow estimation have not been studied. In this paper, we use the 2-D spatial spectrum (i.e., k-space) to describe such effects on both axial and lateral velocity estimations. The proposed k-space modeling on 2-D motion exhibits the following characteristics. Spatial spectrum of an axially moving object is the shifted version of that of a stationary object. The shifted amount is directly related to the axial velocity and increases as the axial spatial frequency increases. The lateral spatial spectrum bandwidth is proportional to the relative lateral motion between the transducer and the object. Based on these properties, an algorithm for 2-D vector velocity estimation is proposed. Both simulations and flow phantom experiments were conducted. A 45- MHz transducer was used and the transducer was scanned at 20 mm/s. The Doppler angles ranged from 29 ° to 90 ° and the flow velocity was between 15 and 30 mm/s. Results show that the proposed k-space velocity estimator had an average angle estimation error of 2.6° and standard deviations from 2.2° to 8.2°. When the swept scan effects were ignored, the average angle estimation error was 14.2° and standard deviations from 1.4° to 3°. Thus, benefits of the proposed k-space vector velocity estimator in high frequency ultrasonic imaging were clearly demonstrated.
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