1 Department of Electrical Engineering, Technical University of Denmark2 Biomedical Engineering, Department of Electrical Engineering, Technical University of Denmark3 Center for Fast Ultrasound Imaging, Center, Technical University of Denmark
The distribution of velocities of blood or tissue is displayed using ultrasound scanners by finding the power spectrum of the received signal. This is currently done by making a Fourier transform of the received signal and then showing spectra in an M-mode display. It is desired to show a B-mode image for orientation, and data for this has to acquired interleaved with the flow data. The power spectrum can be calculated from the Fourier transform of the autocorrelation function Ry (k), where its span of lags k is given by the number of emission N in the data segment for velocity estimation. The lag corresponds to the difference in pulse number, so that for lag k data from emission i is correlated with i + k. The autocorrelation for lag k can be averaged over N-k pairs of emissions. It is possible to calculate Ry (k) for a sparse set of emissions, as long as all combinations of emissions cover all lags in Ry (k). A sparse set of emissions inter-spaced with B-mode emissions can, therefore, be used for estimating Ry (k) The sequence 'v B v v B! gives 2 B-mode emissions (B) for every 3 velocity emissions (v) and is denoted a 3:2 sequence. All combinations on lags are present k='0123..!, if the sequence is continually repeated. The variance on the estimate of Ry (k) is determined by the number of emission pairs for the value of k, and it can be lowered by averaging the RF data over the range gate. Many other sequences can be devised with this property giving 3:3, 3:4, and 5:8 or even random sequences, so that the ratio between B-mode frame rate and spectral precision can be selected.