# Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences

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## Abstract

Ultrasound scanners can be used for displaying the distribution of velocities in blood vessels by finding the power spectrum of the received signal. It is desired to show a B-mode image for orientation and data for this has to be acquired interleaved with the flow data. Techniques for maintaining both the B-mode frame rate, and at the same time have the highest possible $f_{prf}$ only limited by the depth of investigation, are, thus, of great interest. The power spectrum can be calculated from the Fourier transform of the autocorrelation function $R_r(k)$. The lag $k$ corresponds to the difference in pulse number, so that for lag $k$ data from emission $i$ is correlated with $i+k$. It is possible to calculate $R_r(k)$ for a sparse set of emissions, as long as all combinations of emissions cover all lags in $R_r(k)$. A sparse set of emissions interleaved with B-mode emissions can, therefore, be used for estimating $R_r(k)$. The approach has been investigated using Field II simulation of the flow in the carotid and femoral arteries. A 5 MHz linear array transducer with 128 elements, a pitch of $\lambda$ and an element height of 5 mm was simulated. The autocorrelation was calculated from the sparse sequence and averaged over a pulse length. The 1:2 sequence using 2 flow emission for one b-Mode emissions showed a nearly indistinguishable spectrum compared to a Fourier spectrum calculated on the full data. The sparser sequences give a higher noise in the spectrum proportional to the sparseness of the sequence. The audio signal has also been synthesized from the autocorrelation data by passing white, Gaussian noise through a filter designed from the power spectrum of the autocorrelation function. The results show that both the full velocity range can be maintained at the same time as a B-mode image is shown in real time, where the trade-off between B-mode frame rate and spectral accuracy can be selected.
Original language English 2005 IEEE Ultrasonics symposium 1-4 IEEE 2005 141-145 0-7803-9382-1 https://doi.org/10.1109/ULTSYM.2005.1602816 Published - 2005 2005 IEEE Ultrasonics Symposium - Rotterdam, NetherlandsDuration: 18 Sep 2005 → 21 Sep 2005http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=10674

### Conference

Conference 2005 IEEE Ultrasonics Symposium Netherlands Rotterdam 18/09/2005 → 21/09/2005 http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=10674
Series I E E E International Ultrasonics Symposium. Proceedings 1051-0117

## Keywords

• Medical
• Velocity estimation
• Ultrasound

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