Abstract

We present a quantitative comparison of three categories of velocity estimation algorithms, including centroid techniques (the adaptive centroid technique and the weighted centroid technique), the sliding-window filtering technique, and correlation techniques (autocorrelation and cross correlation). We introduce, among these five algorithms, two new algorithms: weighted centroid and sliding-window filtering. Simulations and in vivo blood flow data are used to assess the velocity estimation accuracies of these algorithms. These comparisons demonstrate that the sliding-window filtering technique is superior to the other techniques in terms of velocity estimation accuracy and robustness to noise.

© 2002 Optical Society of America

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  1. X. J. Wang, T. E. Milner, J. S. Nelson, “Characterization of fluid flow velocity by optical Doppler tomography,” Opt. Lett. 20, 1337–1339 (1995).
    [CrossRef] [PubMed]
  2. Z. P. Chen, T. E. Milner, D. Dave, J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett. 22, 64–66 (1997).
    [CrossRef] [PubMed]
  3. Z. P. Chen, T. E. Milner, S. Srinivas, X. J. Wang, A. Malekafzali, M. J. C. van Germert, J. S. Nelson, “Noninvasive imaging of in vivo blood flow velocity using optical Doppler tomography,” Opt. Lett. 22, 14, 1119–1121 (1997).
    [CrossRef]
  4. J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, A. J. Welch, “In vivo bi-directional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. 22, 1439–1441 (1997).
    [CrossRef]
  5. M. D. Kulkarni, T. G. van Leeuwen, S. Yazdanfar, A. J. Welch, J. A. Izatt, “Velocity-estimation accuracy and frame-rate limitations in color Doppler optical coherence tomography,” Opt. Lett. 23, 1057–1059 (1998).
    [CrossRef]
  6. T. G. van Leeuwen, M. D. Kulkarni, S. Yazdanfar, A. M. Rollins, J. A. Izatt, “High-flow-velocity and shear-rate imaging by use of color Doppler optical coherence tomography,” Opt. Lett. 24, 1584–1586 (1999).
    [CrossRef]
  7. Y. H. Zhao, Z. P. Chen, C. Saxer, S. H. Xiang, J. F. de Boer, J. S. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scaning speed and high velocity sensitivity,” Opt. Lett. 25, 114–116 (2000).
    [CrossRef]
  8. Y. H. Zhao, Z. P. Chen, C. Saxer, Q. M. Shen, S. H. Xiang, J. F. de Boer, J. S. Nelson, “Doppler standard deviation imaging for clinical monitoring of in vivo human skin blood flow,” Opt. Lett. 25, 1358–1360 (2000).
    [CrossRef]
  9. S. Yazdanfar, A. M. Rollins, J. A. Izatt, “Imaging and velocimetry of the human retinal circulation with color Doppler optical coherence tomography,” Opt. Lett. 25, 1448–1450 (2000).
    [CrossRef]
  10. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  11. C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
    [CrossRef]
  12. A. M. Rollins, S. Yazdanfar, J. Barton, J. Izatt, “Real-time in vivo color Doppler optical coherence tomography,” J. Biomed. Opt. 7, 123–129 (2002).
    [CrossRef] [PubMed]
  13. L. Hatle, B. Angelsen, Doppler Ultrasound in Cardiology (Lea & Febiger, Philadelphia, 1982).
  14. B. Angelson, “Instantaneous frequency, mean frequency, and variance of mean frequency estimators for ultrasonic blood velocity Doppler signals,” IEEE Trans. Biomed. Eng. BME-28, 733–741 (1981).
    [CrossRef]
  15. G. J. Tearney, B. E. Bouma, J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett. 22, 23, 1811–1813 (1997).
    [CrossRef]
  16. P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

2002 (1)

A. M. Rollins, S. Yazdanfar, J. Barton, J. Izatt, “Real-time in vivo color Doppler optical coherence tomography,” J. Biomed. Opt. 7, 123–129 (2002).
[CrossRef] [PubMed]

2001 (1)

P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

2000 (3)

1999 (1)

1998 (1)

1997 (4)

1995 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1985 (1)

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

1981 (1)

B. Angelson, “Instantaneous frequency, mean frequency, and variance of mean frequency estimators for ultrasonic blood velocity Doppler signals,” IEEE Trans. Biomed. Eng. BME-28, 733–741 (1981).
[CrossRef]

Angelsen, B.

L. Hatle, B. Angelsen, Doppler Ultrasound in Cardiology (Lea & Febiger, Philadelphia, 1982).

Angelson, B.

B. Angelson, “Instantaneous frequency, mean frequency, and variance of mean frequency estimators for ultrasonic blood velocity Doppler signals,” IEEE Trans. Biomed. Eng. BME-28, 733–741 (1981).
[CrossRef]

Barton, J.

A. M. Rollins, S. Yazdanfar, J. Barton, J. Izatt, “Real-time in vivo color Doppler optical coherence tomography,” J. Biomed. Opt. 7, 123–129 (2002).
[CrossRef] [PubMed]

Barton, J. K.

Bouma, B. E.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, Z. P.

Cheng, C. J.

P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

Dave, D.

de Boer, J. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

G. J. Tearney, B. E. Bouma, J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett. 22, 23, 1811–1813 (1997).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hatle, L.

L. Hatle, B. Angelsen, Doppler Ultrasound in Cardiology (Lea & Febiger, Philadelphia, 1982).

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Izatt, J.

A. M. Rollins, S. Yazdanfar, J. Barton, J. Izatt, “Real-time in vivo color Doppler optical coherence tomography,” J. Biomed. Opt. 7, 123–129 (2002).
[CrossRef] [PubMed]

Izatt, J. A.

Kasai, C.

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

Koyano, A.

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

Kulkarni, M. D.

Li, P. C.

P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Malekafzali, A.

Milner, T. E.

Namekawa, K.

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

Nelson, J. S.

Omoto, R.

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rollins, A. M.

Saxer, C.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Shen, Q. M.

Srinivas, S.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

van Germert, M. J. C.

van Leeuwen, T. G.

Wang, X. J.

Welch, A. J.

Xiang, S. H.

Yazdanfar, S.

Yeh, C. K.

P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

Zhao, Y. H.

IEEE Trans. Biomed. Eng. (1)

B. Angelson, “Instantaneous frequency, mean frequency, and variance of mean frequency estimators for ultrasonic blood velocity Doppler signals,” IEEE Trans. Biomed. Eng. BME-28, 733–741 (1981).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

C. Kasai, K. Namekawa, A. Koyano, R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Trans. Sonics Ultrason. SU-32, 458–463 (1985).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

P. C. Li, C. J. Cheng, C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 4, 1084–1091 (2001).

J. Biomed. Opt. (1)

A. M. Rollins, S. Yazdanfar, J. Barton, J. Izatt, “Real-time in vivo color Doppler optical coherence tomography,” J. Biomed. Opt. 7, 123–129 (2002).
[CrossRef] [PubMed]

Opt. Lett. (10)

Y. H. Zhao, Z. P. Chen, C. Saxer, S. H. Xiang, J. F. de Boer, J. S. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scaning speed and high velocity sensitivity,” Opt. Lett. 25, 114–116 (2000).
[CrossRef]

X. J. Wang, T. E. Milner, J. S. Nelson, “Characterization of fluid flow velocity by optical Doppler tomography,” Opt. Lett. 20, 1337–1339 (1995).
[CrossRef] [PubMed]

Z. P. Chen, T. E. Milner, D. Dave, J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett. 22, 64–66 (1997).
[CrossRef] [PubMed]

Z. P. Chen, T. E. Milner, S. Srinivas, X. J. Wang, A. Malekafzali, M. J. C. van Germert, J. S. Nelson, “Noninvasive imaging of in vivo blood flow velocity using optical Doppler tomography,” Opt. Lett. 22, 14, 1119–1121 (1997).
[CrossRef]

J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, A. J. Welch, “In vivo bi-directional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. 22, 1439–1441 (1997).
[CrossRef]

G. J. Tearney, B. E. Bouma, J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett. 22, 23, 1811–1813 (1997).
[CrossRef]

M. D. Kulkarni, T. G. van Leeuwen, S. Yazdanfar, A. J. Welch, J. A. Izatt, “Velocity-estimation accuracy and frame-rate limitations in color Doppler optical coherence tomography,” Opt. Lett. 23, 1057–1059 (1998).
[CrossRef]

T. G. van Leeuwen, M. D. Kulkarni, S. Yazdanfar, A. M. Rollins, J. A. Izatt, “High-flow-velocity and shear-rate imaging by use of color Doppler optical coherence tomography,” Opt. Lett. 24, 1584–1586 (1999).
[CrossRef]

Y. H. Zhao, Z. P. Chen, C. Saxer, Q. M. Shen, S. H. Xiang, J. F. de Boer, J. S. Nelson, “Doppler standard deviation imaging for clinical monitoring of in vivo human skin blood flow,” Opt. Lett. 25, 1358–1360 (2000).
[CrossRef]

S. Yazdanfar, A. M. Rollins, J. A. Izatt, “Imaging and velocimetry of the human retinal circulation with color Doppler optical coherence tomography,” Opt. Lett. 25, 1448–1450 (2000).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (1)

L. Hatle, B. Angelsen, Doppler Ultrasound in Cardiology (Lea & Febiger, Philadelphia, 1982).

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Figures (6)

Fig. 1
Fig. 1

Laminar flow signal simulation. (a) Schematic of the simulation model, (b) amplitude image of simulated 2-D flow signal, (c) 1-D velocity profile pattern of the simulated flow signal, (d) 2-D velocity image of the simulated flow signal.

Fig. 2
Fig. 2

(a) Schematic of the ODT system: O1, microscope objective lens; O2, GRIN lens; G, galvanometer; L, achromatic lens. (b) Illustration of scanning optical delay line by Littrow-mounting of diffraction grating: f, focal length; γ, the total rotation angle of the mirror; α, the divergence angle of the reflected light from the lens axis; r, the displacement of light from the lens axis at the surface of the lens; θ L , Littrow angle; Δl, the resulting optical delay.

Fig. 3
Fig. 3

Estimation accuracy as a function of the SNR of five estimation techniques.

Fig. 4
Fig. 4

Comparison of simulated flow profile with the actual flow profile at a SNR = 20 dB. In each figure (a) adaptive centroid algorithm, (b) weighted centroid algorithm, (c) sliding-window filtering algorithm, (d) autocorrelation algorithm, (e) cross-correlation algorithm, the solid curve corresponds to the estimated velocity profile at k = 13 [k is the lateral dimension at Fig. 1(d)], and the dotted curve is the actual profile. The centroid techniques (a) and (b) provide accurate estimates, while they are sensitive to noise. The filtering technique (c) is more accurate and robust to noise. The correlation techniques (d) and (e) provide reasonably accurate velocity estimates at a high-velocity region but overestimate at low-flow velocity regions.

Fig. 5
Fig. 5

Comparison of the simulated flow profile with the actual flow profile at a SNR = 6 dB. In each figure (a) adaptive centroid algorithm, (b) weighted centroid algorithm, (c) sliding-window filtering algorithm, (d) autocorrelation algorithm, (e) cross-correlation algorithm, the solid curve corresponds to the estimated velocity profile at k = 13 [k is the lateral dimension at Fig. 1(d)], and the dotted curve is the actual profile. Again, the weighed centroid algorithm is slightly less noisy than the adaptive centroid one while they have similar accuracy. The correlation techniques (d) and (e) show less accurate estimates in both high and low flow regions at this low SNR, but the techniques are free of noise spikes compared with the results of centroid techniques (a) and (b). Apparently, the filtering technique (c) has the best estimation at this low SNR in terms of accuracy and robustness to noise.

Fig. 6
Fig. 6

Comparison of flow velocity estimation algorithms based on in vivo blood flow. The same noise-threshold and color-threshold levels are applied in each image to highlight the flow region. The black bar under each image represents a scale of 250 µm. (a) Structural image, (b) blood-flow image by the adaptive centroid estimation, (c) blood-flow image by the weighted centroid estimation, (d) blood-flow image by the sliding-window filtering estimation, (e) blood-flow image by autocorrelation.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

z˜k,it=|z˜k,it|expjωt,
υs=ωsω0c2μg cos θ,
ω¯k,i=- ωPk,iωdω- Pk,iωdω.
Pnk,iω=STFTk,itn, ωSTFTk,itn, ω¯,
ω¯k,in=- ωPnk,iωdω- Pnk,iωdω.
ω¯k,in=ωp-Δω/2ωp+Δω/2 ωPnk,iωdωωp-Δω/2ωp+Δω/2 Pnk,iωdω,
Δf=2V0-VsΔν/c
ω¯k,in=- ωPnk,iωξdω-Pnk,iωξdω,
Rnk,iτ=tn-Ntstn z˜k,it+τ×z˜k,it¯dt,
Rnk,iτ=|Rnk,iτ|expjϕk,inτ,
ω¯k,in=ϕ˙nk,i0ϕnk,iΔTΔT1ΔTtan-1ImRnk,iΔTReRnk,iΔT,
Cnk,iT=tn-NTtn Z˜k,it+T×Z˜k+1,it¯dt,
Cnk,iτ=|Cnk,iτ|expjϕnk,iτ,
ω¯k,inϕnk,iTT1Ttan-1ImCnk,iTReCnk,iT.
Vr=d2Δp16μΔL1-2rd2,
Z˜k,itn=S˜ktn, ti  F-1kω-ωnΔω, ω-ωnΔω+N˜ktn, ti,
Δl=2f tanθLtanγ,
Δl=2fγ tanθL=2fΓ tanθLt.

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