K-space model of motion artifacts in synthetic transmit ultrasound imaging

Synthetic transmit aperture (STA) imaging gives the possibility to acquire an image with only few emissions and is appealing for 3D ultrasound imaging. Even though the number of emissions is low, the change in position of the scatterers prohibits the coherent summations of ultrasound echoes and leads to distortions in the image. In order to develop motion compensation and/or velocity estimation algorithms a thorough and intuitive understanding of the nature of motion artifacts is needed. This paper proposes a simple 2D broad band model for STA images, based on the acquisition procedure and the beamformation algorithm. In STA imaging a single element transmits a cylindrical wave. All elements are used in receive, and by applying different delays a low resolution image (LRI) is beamformed. A Fourier relation exists between the aperture function and all points in the beamformed LRI. This relation is used to develop an approximation of the point spread function (PSF) of a LRI. It is shown that the PSF of LRIs obtained by transmitting with different elements can be viewed as rotated versions of each other. Summing several LRIs gives a high resolution image. The model approximates the PSF of a high resolution image as a sum of rotated PSFs of a single LRI. The approximation is validated with a Field II simulation. The model predicts and explains the motion artifacts, and gives an intuitive feeling of what would happen for different velocities.