Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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 languageEnglish
Title of host publication2005 IEEE Ultrasonics symposium
Volume1-4
PublisherIEEE
Publication date2005
Pages141-145
ISBN (Print)0-7803-9382-1
DOIs
Publication statusPublished - 2005
Event2005 IEEE Ultrasonics Symposium - Rotterdam, Netherlands
Duration: 18 Sep 200521 Sep 2005
http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=10674

Conference

Conference2005 IEEE Ultrasonics Symposium
CountryNetherlands
CityRotterdam
Period18/09/200521/09/2005
Internet address
SeriesI E E E International Ultrasonics Symposium. Proceedings
ISSN1051-0117

Keywords

  • Medical
  • Velocity estimation
  • Ultrasound

Cite this

Jensen, J. A. (2005). Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences. In 2005 IEEE Ultrasonics symposium (Vol. 1-4, pp. 141-145). IEEE. I E E E International Ultrasonics Symposium. Proceedings https://doi.org/10.1109/ULTSYM.2005.1602816
Jensen, Jørgen Arendt. / Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences. 2005 IEEE Ultrasonics symposium. Vol. 1-4 IEEE, 2005. pp. 141-145 (I E E E International Ultrasonics Symposium. Proceedings).
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title = "Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences",
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.",
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Jensen, JA 2005, Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences. in 2005 IEEE Ultrasonics symposium. vol. 1-4, IEEE, I E E E International Ultrasonics Symposium. Proceedings, pp. 141-145, 2005 IEEE Ultrasonics Symposium, Rotterdam, Netherlands, 18/09/2005. https://doi.org/10.1109/ULTSYM.2005.1602816

Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences. / Jensen, Jørgen Arendt.

2005 IEEE Ultrasonics symposium. Vol. 1-4 IEEE, 2005. p. 141-145 (I E E E International Ultrasonics Symposium. Proceedings).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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AB - 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.

KW - Medical

KW - Velocity estimation

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M3 - Article in proceedings

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EP - 145

BT - 2005 IEEE Ultrasonics symposium

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Jensen JA. Spectral Velocity Estimation using the Autocorrelation Function and Sparse data Sequences. In 2005 IEEE Ultrasonics symposium. Vol. 1-4. IEEE. 2005. p. 141-145. (I E E E International Ultrasonics Symposium. Proceedings). https://doi.org/10.1109/ULTSYM.2005.1602816