Abstract

In this paper, we develop a random process theory to explain the laser speckle phenomena. The relation between the probability distribution of speckle’s integrated intensity random process Y(t) and the relative velocity v(t) is derived. Based on the random process theory, traditional spatial or temporal laser speckle contrast analysis (i.e. spatial or temporal LASCA) can be derived as the spatial or temporal estimators respectively. Both spatial LASCA and temporal LASCA suffer from noise due to insufficient statistics and nonstationarity in either spatial or temporal domain. Furthermore, either LASCA results in a reduction of spatial or temporal resolution. A new random process estimator is proposed and able to overcome these drawbacks. In an in-vitro study, random process estimator outperforms either spatial LASCA or temporal LASCA by providing much higher SNR (random process estimator vs. spatial LASCA vs. temporal LASCA: 33.64±6.87 (mean±s.t.d.) vs. 9.08±2.85 vs. 3.83±1.05). In an in-vivo structural imaging study, random process estimator efficiently suppresses the noise in contrast image and thus improves the distinguishability of small vessels. In a functional imaging study of cerebral blood flow change in the somatosensory cortex induced by rat’s hind paw stimulation, random process estimator provides much lower estimation errors in single trial data (random process estimator vs. temporal LASCA: 0.31±0.03 vs. 1.36±0.09) and finally leads to higher resolution spatiotemporal patterns of cerebral blood flow.

© 2009 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
    [CrossRef]
  5. A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
    [CrossRef] [PubMed]
  6. T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (2)

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

H. Cheng, Y. Yan, and T. Q. Duong, “Laser speckle imaging of rat retinal blood flow with hybrid temporal and spatial analysis method,” Proc. SPIE 7163, 716304 (2009).
[CrossRef]

2008 (2)

H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
[CrossRef]

A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (1)

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

2004 (2)

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

2003 (2)

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

P. K. Dixon and D. J. Durian, “Speckle Visibility Spectroscopy and Variable Granular Fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[CrossRef] [PubMed]

2001 (2)

J. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22(4), 35–66 (2001).
[CrossRef]

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

1996 (1)

J. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996).
[CrossRef]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

1981 (1)

A. Fercher and J. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981).
[CrossRef]

Bandyopadhyay, R.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

Bezerianos, A.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Boas, D.

Boas, D. A.

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

Bolay, H.

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

Briers, J.

J. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22(4), 35–66 (2001).
[CrossRef]

J. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996).
[CrossRef]

A. Fercher and J. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981).
[CrossRef]

Brown, B. R.

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

Buck, A.

Burnett, M. G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Cen, J.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Chen, S.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Cheng, H.

H. Cheng, Y. Yan, and T. Q. Duong, “Laser speckle imaging of rat retinal blood flow with hybrid temporal and spatial analysis method,” Proc. SPIE 7163, 716304 (2009).
[CrossRef]

H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
[CrossRef]

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Cui, H.

Detre, J. A.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Dixon, P.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

Dixon, P. K.

P. K. Dixon and D. J. Durian, “Speckle Visibility Spectroscopy and Variable Granular Fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[CrossRef] [PubMed]

Dunn, A. K.

A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008).
[CrossRef] [PubMed]

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

Duong, T.

H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
[CrossRef]

Duong, T. Q.

H. Cheng, Y. Yan, and T. Q. Duong, “Laser speckle imaging of rat retinal blood flow with hybrid temporal and spatial analysis method,” Proc. SPIE 7163, 716304 (2009).
[CrossRef]

Durduran, T.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Durian, D.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

P. Lemieux and D. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A 16(7), 1651–1664 (1999).
[CrossRef]

Durian, D. J.

P. K. Dixon and D. J. Durian, “Speckle Visibility Spectroscopy and Variable Granular Fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[CrossRef] [PubMed]

Easley, K. A.

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

Fercher, A.

A. Fercher and J. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981).
[CrossRef]

Fontenelle, H.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Furuya, D.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Gittings, A.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

Gong, H.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Gopal, A.

Greenberg, J. H.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Jones, S. C.

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

Kharlamov, A.

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

Lemieux, P.

Li, M.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Lu, W.

Luo, Q.

D. Zhu, W. Lu, Y. Weng, H. Cui, and Q. Luo, “Monitoring thermal-induced changes in tumor blood flow and microvessels with laser speckle contrast imaging,” Appl. Opt. 46(10), 1911–1917 (2007).
[CrossRef] [PubMed]

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Miao, P.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Moskowitz, M. A.

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

Parthasarathy, A. B.

Pine, D. J.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Qiu, Y.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Scheffold, F.

Suh, S.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

Tom, W. J.

Tong, S.

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

Völker, A.

Weber, B.

Webster, S.

J. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996).
[CrossRef]

Weitz, D. A.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Weng, Y.

Yan, Y.

H. Cheng, Y. Yan, and T. Q. Duong, “Laser speckle imaging of rat retinal blood flow with hybrid temporal and spatial analysis method,” Proc. SPIE 7163, 716304 (2009).
[CrossRef]

H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
[CrossRef]

Yodh, A.

Yodh, A. G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Yu, G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Zakharov, P.

Zeng, S.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

Zhang, X.

Zhou, C.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

Zhu, D.

Appl. Opt. (1)

IEEE Trans. Biomed. Eng. (1)

P. Miao, M. Li, H. Fontenelle, A. Bezerianos, Y. Qiu, and S. Tong, “Imaging the Cerebral Blood Flow with Enhanced Laser Speckle Contrast Analysis (eLASCA) by Monotonic Point Transformation,” IEEE Trans. Biomed. Eng. 56(4), 1127–1133 (2009).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

J. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996).
[CrossRef]

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab. (2)

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, “Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry,” J. Cereb. Blood Flow Metab. 24(5), 518–525 (2004).
[CrossRef] [PubMed]

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Neurosci. Lett. (1)

A. Kharlamov, B. R. Brown, K. A. Easley, and S. C. Jones, “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett. 368(2), 151–156 (2004).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Fercher and J. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981).
[CrossRef]

Opt. Express (2)

H. Cheng, Y. Yan, and T. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 214–219 (2008).
[CrossRef]

A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Physiol. Meas. (1)

J. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22(4), 35–66 (2001).
[CrossRef]

Proc. SPIE (1)

H. Cheng, Y. Yan, and T. Q. Duong, “Laser speckle imaging of rat retinal blood flow with hybrid temporal and spatial analysis method,” Proc. SPIE 7163, 716304 (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

The denoising performance of random process estimator: (a) one frame of raw images; (b) the estimation results of σ Y using different methods; (c) the contrast image K Y 2 estimated based on all 600 raw images using the random process estimator; (d) the estimated K Y 2 using different methods.

Fig. 2
Fig. 2

Structural imaging of rat’s cerebral blood vessels: (a, b, c) show the contrast images K Y 2 estimated from the first 2, 10 and 80 frames using random process estimator; (d, e, f) show the contrast images K Y 2 estimated from the first 2, 10 and 80 frames using temporal LASCA.

Fig. 3
Fig. 3

Denoising performance of random process estimator for structural imaging: the contrast values K Y 2 along the vertical line in Fig. 2 (c) estimated from different number of frames: N=2 (a), N=10 (b), N=80 (c) using random process estimator and temporal LASCA.

Fig. 4
Fig. 4

Spatiotemporal change of K Y 2 during the pre-stimulation stage: the first row shows the K 20 2 , F 19 , , F 16 (from the left to the right) using random process estimator; the second raw shows the K 20 2 , F 19 , , F 16 (from the left to the right) using temporal LASCA.

Fig. 5
Fig. 5

The averaged errors of single trial result using temporal LASCA and random process estimator respectively.

Fig. 6
Fig. 6

The changing patterns of CBF under functional stimulation calculated by random process estimator.

Fig. 7
Fig. 7

The changing patterns of CBF under functional stimulation calculated by temporal LASCA.

Fig. 8
Fig. 8

The functional changes of contrast values corresponding to the pixel designated by a white circle in the first frame of Fig. 6: (a) the averaged changes, i.e. F ¯ n , n = 19 , , 59 s , using temporal LASCA and random process estimator; (b) the standard deviation of the F n , n = 19 , , 59 s across all ten trials using temporal LASCA and random process estimator.

Fig. 9
Fig. 9

Gaussian assumptions confirmed by the data acquired in the in-vitro experiment: (a) the pdf of N A σ s ; (b) the P-P plot of all 600 N A σ s s; (c) the pdf of N A μ s ; (d) the P-P plot of all 600 N A μ s s.

Fig. 10
Fig. 10

The vascular details in the white box area in (a) using hybrid method with 5 × 5 (b) and 3 × 3 (c) spatial window, random process estimator (d).

Fig. 11
Fig. 11

The functional CBF changes of selected area in (a) at the 8th sec estimated by temporal LASCA (b) as in Fig. 7, hybrid method (c) and random process estimator (d) as in Fig. 6.

Equations (21)

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g 1 ( τ ) = E ( t ) E * ( t τ ) t e m p o r a l / E ( t ) E * ( t ) t e m p o r a l .
I ˜ ( t ) = 1 T t t + T I ( t ) d t
μ Y ( t 1 ) Y ( t 1 ) e n s e m b l e = 1 T t 1 t 1 + T X ( t ) d t e n s e m b l e = 1 T t 1 t 1 + T X ( t ) e n s e m b l e d t μ X ( t 1 )
g 2 ( τ ) = X ( t ) X ( t τ ) t e m p o r a l / X ( t ) t e m p o r a l 2 .
X ( t ) X ( t τ ) t e m p o r a l = X ( t 1 ) e n s e m b l e 2 ( 1 + β | g 1 ( τ ) | 2 ) ,
Y 2 ( t 1 ) ensemble = 1 T 2 t 1 t 1 +T t 1 t 1 +T X ( t )X( t )d t d t ensemble                       1 T 2 t 1 t 1 +T t 1 t 1 +T X( t )X( t ) temporal d t d t ensemble                      = 1 T 2 t 1 t 1 +T t 1 t 1 +T (1+β | g 1 ( t t ) | 2 )d t d t X( t 1 ) ensemble 2 ensemble                      = 1 T 2 ( T 2 + 0 T 0 T β | g 1 ( t t ) | 2 d t d t ) μ X 2 ( t 1 ) ensemble                      = 1 T 2 ( T 2 + 0 T 0 T β | g 1 ( t t ) | 2 d t d t ) μ Y 2 ( t 1 )                      = Y( t 1 ) ensemble 2 (1+ β T 0 T 2 (1 τ T ) g 1 2 (τ)dτ)
Y 2 ( t 1 ) e n s e m b l e Y ( t 1 ) e n s e m b l e 2 Y ( t 1 ) e n s e m b l e 2 = β T 0 T 2 ( 1 τ T ) g 1 2 ( τ ) d τ .
K Y 2 ( t 1 ) = σ Y 2 ( t 1 ) μ Y 2 ( t 1 ) = β T 0 T 2 ( 1 τ T ) g 1 2 ( τ ) d τ ,
K s p a t i a l 2 ( t 1 ) = σ s 2 ( t 1 ) μ s 2 ( t 1 ) K Y 2 ( t 1 )
μ s ( t 1 ) = μ Y ( t 1 ) + N A μ s ( t 1 ) + N B μ s ( t 1 ) ,
σ s ( t 1 ) = σ Y ( t 1 ) + N A σ s ( t 1 ) + N B σ s ( t 1 ) .
I ˜ ( t 1 + n Δ t ) = 1 T t 1 + n Δ t t 1 + n Δ t + T I ( t ) d t ,
K t e m p o r a l 2 ( t 1 ) = σ t 2 ( t 1 ) μ t 2 ( t 1 ) K Y 2 ( t 1 ) ,
μ t ( t 1 ) = μ Y ( t 1 ) + N A μ t ( t 1 ) + N B μ t ( t 1 ) ,
σ t ( t 1 ) = σ Y ( t 1 ) + N A σ t ( t 1 ) + N B σ t ( t 1 ) .
σ r p e ( t 1 ) = 1 N n = 0 N 1 σ s ( t 1 + n Δ t ) = σ ¯ Y ( t 1 ) + 1 N n = 0 N 1 N A σ s ( t 1 + n Δ t ) ,
μ r p e ( t 1 ) = 1 N n = 0 N 1 I ˜ ( t 1 + n Δ t ) = 1 N n = 0 N 1 μ Y ( t 1 + n Δ t ) + 1 N n = 0 N 1 N A μ s ( t 1 + n Δ t ) .
K r p e 2 ( t 1 ) = σ r p e 2 ( t 1 ) μ r p e 2 ( t 1 ) σ ¯ Y 2 ( t 1 ) μ ¯ Y 2 ( t 1 ) = K Y 2 ( t 1 ) .
S N R = ( A s i g n a l A n o i s e ) 2 = ( K Y 2 [ 1 T n = 0 T 1 ( K e s t i m a t i o n 2 ( n ) K Y 2 ) 2 ] 1 / 2 ) 2 ,
F n = K 20 2 K n 2 K 20 2 × 100 % ,
E r r o r F n = ( 1 N r o w N c o l x = 1 N r o w y = 1 N c o l F n 2 ( x , y ) ) 1 / 2 ,

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