Abstract

In this paper, we formulate diffuse optical tomography (DOT) problems as a source localization problem and propose a MUltiple SIgnal Classification (MUSIC) algorithm for functional brain imaging application. By providing MUSIC spectra for major chromophores such as oxy-hemoglobin (HbO) and deoxy-hemoglobin (HbR), we are able to investigate the spatial distribution of brain activities. Moreover, the false discovery rate (FDR) algorithm can be applied to control the family-wise error in the MUSIC spectra. The minimum distance between the center of mass in DOT and the Montreal Neurological Institute (MNI) coordinates of target regions in experiments was between approximately 6 and 18mm, and the displacement of the center of mass in DOT and fMRI ranged between 12 and 28mm, which demonstrate the legitimacy of the DOT-based imaging. The proposed brain mapping method revealed its potential as an alternative algorithm to monitor the brain activation.

© 2012 OSA

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2012 (1)

J. M. Kim, O. K. Lee, and J. C. Ye, “Compressive MUSIC: revisiting the link between compressive sensing and array signal processing,” IEEE Trans. Inf. Theory 58, 278–301 (2012).
[CrossRef]

2011 (3)

O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30, 1129–1142 (2011).
[CrossRef]

T. Li, H. Gong, and Q. Luo, “Visualization of light propagation in visible Chinese human head for functional near-infrared spectroscopy,” J. Biomed. Opt. 16, 045001 (2011).
[CrossRef] [PubMed]

T. Takahashi, Y. Takikawa, R. Kawagoe, S. Shibuya, T. Iwano, and S. Kitazawa, “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).
[CrossRef] [PubMed]

2010 (5)

N. M. Gregg, B. R. White, B. W. Zeff, A. J. Berger, and J. P. Culver, “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front Neuroenergetics 2, 1–8 (2010).

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef] [PubMed]

F. Abdelnour, C. Genovese, and T. Huppert, “Hierarchical Bayesian regularization of reconstructions for diffuse optical tomography using multiple priors,” Biomed. Opt. Express 1, 1084–1103 (2010).
[CrossRef]

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. Eric, L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

2009 (6)

A. Fletcher, S. Rangan, and V. Goyal, “Necessary and sufficient conditions for sparsity pattern recovery,” IEEE Trans. Inf. Theory 55, 5758–5772 (2009).
[CrossRef]

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, D137–D143 (2009).
[CrossRef] [PubMed]

K. E. Jang, S. Tak, J. Jung, J. Jang, and J. C. Ye, “Wavelet minimum description length detrending for near-infrared spectroscopy,” J. Biomed. Opt. 14, 034004 (2009).
[CrossRef] [PubMed]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef] [PubMed]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: Statistical parametric mapping for near-infrared spectroscopy,” NeuroImage 44, 428–447 (2009).
[CrossRef]

2007 (1)

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Nat. Acad. Sci. USA 104, 12169–12174 (2007).
[CrossRef] [PubMed]

2006 (7)

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11, 064029 (2006).
[CrossRef]

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

A. Singh and I. Dan, “Exploring the false discovery rate in multichannel NIRS,” NeuroImage 33, 542–549 (2006).
[CrossRef] [PubMed]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Information Theory 52, 1289–1306 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

J. Chen and X. Huo, “Theoretical results on sparse representations of multiple measurement vectors,” IEEE Trans. Signal Process. 54, 4634–4643 (2006).
[CrossRef]

2005 (3)

N. Okui and E. Okada, “Wavelength dependence of crosstalk in dual-wavelength measurement of oxy- and deoxy-hemoglogin,” J. Biomed. Opt. 10, 011015 (2005).
[CrossRef]

Y. Zhang, D. H. Brooks, and D. A. Boas, “A haemodynamic response function model in spatio-temporal diffuse optical tomography,” Phys. Med. Biol. 50, 4625–4644 (2005).
[CrossRef] [PubMed]

D. A. Boas and A. M. Dale, “Simulation study of magnetic resonance imaging-guided cortically constrained diffuse optical tomography of human brain function,” Appl. Opt. 44, 1957–1968 (2005).
[CrossRef] [PubMed]

2004 (1)

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

2003 (4)

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nature Medicine 9, 123–128 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, S. Prince, S. R. Arridge, and J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, and S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

E. Okada and D. T. Delpy, “Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal,” Appl. Opt. 42, 2915–2922 (2003).
[CrossRef] [PubMed]

2002 (1)

C. Genovese, N. Lazar, and T. Nichols, “Thresholding of statistical maps in functional neuroimaging using the false discovery rate,” NeuroImage 15, 870–878 (2002).
[CrossRef] [PubMed]

2001 (2)

V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res 3, 41–46 (2001).
[CrossRef] [PubMed]

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001).
[CrossRef] [PubMed]

2000 (2)

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

K. J. Friston, O. Josephs, E. Zarahn, A. P. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? bias and efficiency in fmri time-series analysis,” NeuroImage 12, 196–208 (2000).
[CrossRef] [PubMed]

1998 (1)

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43, 2465–2478 (1998).
[CrossRef] [PubMed]

1997 (1)

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

1996 (1)

H. Krim and M. Viberg, “Two decades of array signal processing research,” IEEE Signal Proc. Mag. pp. 67–94 (1996).
[CrossRef]

1995 (1)

Y. Benjamini and Y. Hochberg, “Controlling the flase discovery rate: a practical and powerful approach to multiple testing,” J. R. Stat. Soc. Ser B (Methodl.) 57, 289–300 (1995).

1992 (2)

J. Mosher, P. Lewis, and R. Leahy, “Multiple dipole modelling and localization from spatio-temporal MEG data,” IEEE Trans. Biomed. Eng. 39, 541–557 (1992).
[CrossRef] [PubMed]

S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. Kim, H. Merkle, and K. Ugurbil, “Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging,” Proc. Nati. Acad. Sci. USA 89, 5951–5955 (1992).
[CrossRef]

1990 (1)

W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989 (1)

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer-Rao bound,” IEEE Trans. Acoust., Speech, Signal Process. 37, 720–741 (1989).
[CrossRef]

1986 (1)

R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280 (1986).
[CrossRef]

Aalders, M. C.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. pp. 967–981 (1999).
[CrossRef] [PubMed]

Abdelnour, F.

Abdoulaev, G.

Arridge, S. R.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

V. Kolehmainen, S. Prince, S. R. Arridge, and J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, and S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Ashburner, J.

K. J. Friston, J. Ashburner, S. Kiebel, T. Nichols, and W. Penny, eds., Statistical parametric mapping: The analysis of functional brain images (Academic Press, Sandiego, CA, USA, 2006).

Austin, T.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

Barbour, R. L.

Benaron, D. A.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Benjamini, Y.

Y. Benjamini and Y. Hochberg, “Controlling the flase discovery rate: a practical and powerful approach to multiple testing,” J. R. Stat. Soc. Ser B (Methodl.) 57, 289–300 (1995).

Berger, A. J.

N. M. Gregg, B. R. White, B. W. Zeff, A. J. Berger, and J. P. Culver, “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front Neuroenergetics 2, 1–8 (2010).

Bluestone, A. Y.

Boas, D.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, and S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Boas, D. A.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. Eric, L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef] [PubMed]

D. A. Boas and A. M. Dale, “Simulation study of magnetic resonance imaging-guided cortically constrained diffuse optical tomography of human brain function,” Appl. Opt. 44, 1957–1968 (2005).
[CrossRef] [PubMed]

Y. Zhang, D. H. Brooks, and D. A. Boas, “A haemodynamic response function model in spatio-temporal diffuse optical tomography,” Phys. Med. Biol. 50, 4625–4644 (2005).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

Boden, S.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

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K. J. Friston, J. Ashburner, S. Kiebel, T. Nichols, and W. Penny, eds., Statistical parametric mapping: The analysis of functional brain images (Academic Press, Sandiego, CA, USA, 2006).

Niu, H.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef] [PubMed]

Ntziachristos, V.

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nature Medicine 9, 123–128 (2003).
[CrossRef] [PubMed]

V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res 3, 41–46 (2001).
[CrossRef] [PubMed]

Obrig, H.

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Ogawa, S.

S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. Kim, H. Merkle, and K. Ugurbil, “Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging,” Proc. Nati. Acad. Sci. USA 89, 5951–5955 (1992).
[CrossRef]

Okada, E.

Okui, N.

N. Okui and E. Okada, “Wavelength dependence of crosstalk in dual-wavelength measurement of oxy- and deoxy-hemoglogin,” J. Biomed. Opt. 10, 011015 (2005).
[CrossRef]

Penny, W.

K. J. Friston, J. Ashburner, S. Kiebel, T. Nichols, and W. Penny, eds., Statistical parametric mapping: The analysis of functional brain images (Academic Press, Sandiego, CA, USA, 2006).

Petersen, S. E.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

Poline, J.-B.

K. J. Friston, O. Josephs, E. Zarahn, A. P. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? bias and efficiency in fmri time-series analysis,” NeuroImage 12, 196–208 (2000).
[CrossRef] [PubMed]

Prahl, S. A.

W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Prince, S.

V. Kolehmainen, S. Prince, S. R. Arridge, and J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, and S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Raichle, M. E.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

Rangan, S.

A. Fletcher, S. Rangan, and V. Goyal, “Necessary and sufficient conditions for sparsity pattern recovery,” IEEE Trans. Inf. Theory 55, 5758–5772 (2009).
[CrossRef]

Romberg, J.

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Rouquette, S.

K. J. Friston, O. Josephs, E. Zarahn, A. P. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? bias and efficiency in fmri time-series analysis,” NeuroImage 12, 196–208 (2000).
[CrossRef] [PubMed]

S, B. L.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

Schlaggar, B. L.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Nat. Acad. Sci. USA 104, 12169–12174 (2007).
[CrossRef] [PubMed]

Schmidt, R.

R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280 (1986).
[CrossRef]

Schmitz, C. H.

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001).
[CrossRef] [PubMed]

Schweiger, M.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

Shibuya, S.

T. Takahashi, Y. Takikawa, R. Kawagoe, S. Shibuya, T. Iwano, and S. Kitazawa, “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).
[CrossRef] [PubMed]

Simpson, C. R.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43, 2465–2478 (1998).
[CrossRef] [PubMed]

Singh, A.

A. Singh and I. Dan, “Exploring the false discovery rate in multichannel NIRS,” NeuroImage 33, 542–549 (2006).
[CrossRef] [PubMed]

Snyder, A. Z.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

Steinbrink, J.

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. pp. 967–981 (1999).
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Stevenson, D. K.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Stoica, P.

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer-Rao bound,” IEEE Trans. Acoust., Speech, Signal Process. 37, 720–741 (1989).
[CrossRef]

Tak, S.

K. E. Jang, S. Tak, J. Jung, J. Jang, and J. C. Ye, “Wavelet minimum description length detrending for near-infrared spectroscopy,” J. Biomed. Opt. 14, 034004 (2009).
[CrossRef] [PubMed]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: Statistical parametric mapping for near-infrared spectroscopy,” NeuroImage 44, 428–447 (2009).
[CrossRef]

Takahashi, T.

T. Takahashi, Y. Takikawa, R. Kawagoe, S. Shibuya, T. Iwano, and S. Kitazawa, “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).
[CrossRef] [PubMed]

Takikawa, Y.

T. Takahashi, Y. Takikawa, R. Kawagoe, S. Shibuya, T. Iwano, and S. Kitazawa, “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).
[CrossRef] [PubMed]

Tank, D. W.

S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. Kim, H. Merkle, and K. Ugurbil, “Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging,” Proc. Nati. Acad. Sci. USA 89, 5951–5955 (1992).
[CrossRef]

Tao, T.

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Tian, F.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef] [PubMed]

Tizzard, A.

Toronov, V.

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11, 064029 (2006).
[CrossRef]

Tsuzuki, D.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. Eric, L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Ugurbil, K.

S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. Kim, H. Merkle, and K. Ugurbil, “Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging,” Proc. Nati. Acad. Sci. USA 89, 5951–5955 (1992).
[CrossRef]

van Houten, J. C.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Viberg, M.

H. Krim and M. Viberg, “Two decades of array signal processing research,” IEEE Signal Proc. Mag. pp. 67–94 (1996).
[CrossRef]

Villringer, A.

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

Webb, A.

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11, 064029 (2006).
[CrossRef]

Weissleder, R.

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nature Medicine 9, 123–128 (2003).
[CrossRef] [PubMed]

Welch, A. J.

W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wells, W.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. Eric, L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

White, B. R.

N. M. Gregg, B. R. White, B. W. Zeff, A. J. Berger, and J. P. Culver, “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front Neuroenergetics 2, 1–8 (2010).

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, D137–D143 (2009).
[CrossRef] [PubMed]

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Nat. Acad. Sci. USA 104, 12169–12174 (2007).
[CrossRef] [PubMed]

Wyatt, J. S.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

Ye, J. C.

J. M. Kim, O. K. Lee, and J. C. Ye, “Compressive MUSIC: revisiting the link between compressive sensing and array signal processing,” IEEE Trans. Inf. Theory 58, 278–301 (2012).
[CrossRef]

O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30, 1129–1142 (2011).
[CrossRef]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: Statistical parametric mapping for near-infrared spectroscopy,” NeuroImage 44, 428–447 (2009).
[CrossRef]

K. E. Jang, S. Tak, J. Jung, J. Jang, and J. C. Ye, “Wavelet minimum description length detrending for near-infrared spectroscopy,” J. Biomed. Opt. 14, 034004 (2009).
[CrossRef] [PubMed]

Zarahn, E.

K. J. Friston, O. Josephs, E. Zarahn, A. P. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? bias and efficiency in fmri time-series analysis,” NeuroImage 12, 196–208 (2000).
[CrossRef] [PubMed]

Zeff, B. W.

N. M. Gregg, B. R. White, B. W. Zeff, A. J. Berger, and J. P. Culver, “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front Neuroenergetics 2, 1–8 (2010).

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, D137–D143 (2009).
[CrossRef] [PubMed]

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Nat. Acad. Sci. USA 104, 12169–12174 (2007).
[CrossRef] [PubMed]

Zhang, X.

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11, 064029 (2006).
[CrossRef]

Zhang, Y.

Y. Zhang, D. H. Brooks, and D. A. Boas, “A haemodynamic response function model in spatio-temporal diffuse optical tomography,” Phys. Med. Biol. 50, 4625–4644 (2005).
[CrossRef] [PubMed]

Appl. Opt. (3)

Biomed. Opt. Express (1)

Breast Cancer Res (1)

V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res 3, 41–46 (2001).
[CrossRef] [PubMed]

Front Neuroenergetics (2)

N. M. Gregg, B. R. White, B. W. Zeff, A. J. Berger, and J. P. Culver, “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front Neuroenergetics 2, 1–8 (2010).

S. P. Koch, C. Habermehl, J. Mehnert, C. H. Schmitz, S. Holtze, A. Villringer, J. Steinbrink, and H. Obrig, “High-resolution optical functional mapping of the human somatosensory cortex,” Front Neuroenergetics 2, 1–8 (2010).

IEEE J. Quantum Electron. (1)

W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Signal Proc. Mag. (1)

H. Krim and M. Viberg, “Two decades of array signal processing research,” IEEE Signal Proc. Mag. pp. 67–94 (1996).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (1)

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer-Rao bound,” IEEE Trans. Acoust., Speech, Signal Process. 37, 720–741 (1989).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280 (1986).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

J. Mosher, P. Lewis, and R. Leahy, “Multiple dipole modelling and localization from spatio-temporal MEG data,” IEEE Trans. Biomed. Eng. 39, 541–557 (1992).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (3)

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

J. M. Kim, O. K. Lee, and J. C. Ye, “Compressive MUSIC: revisiting the link between compressive sensing and array signal processing,” IEEE Trans. Inf. Theory 58, 278–301 (2012).
[CrossRef]

A. Fletcher, S. Rangan, and V. Goyal, “Necessary and sufficient conditions for sparsity pattern recovery,” IEEE Trans. Inf. Theory 55, 5758–5772 (2009).
[CrossRef]

IEEE Trans. Information Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Information Theory 52, 1289–1306 (2006).
[CrossRef]

IEEE Trans. Med. Imag. (1)

O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30, 1129–1142 (2011).
[CrossRef]

IEEE Trans. Signal Process. (1)

J. Chen and X. Huo, “Theoretical results on sparse representations of multiple measurement vectors,” IEEE Trans. Signal Process. 54, 4634–4643 (2006).
[CrossRef]

J. Biomed. Opt. (5)

N. Okui and E. Okada, “Wavelength dependence of crosstalk in dual-wavelength measurement of oxy- and deoxy-hemoglogin,” J. Biomed. Opt. 10, 011015 (2005).
[CrossRef]

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef] [PubMed]

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11, 064029 (2006).
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T. Li, H. Gong, and Q. Luo, “Visualization of light propagation in visible Chinese human head for functional near-infrared spectroscopy,” J. Biomed. Opt. 16, 045001 (2011).
[CrossRef] [PubMed]

K. E. Jang, S. Tak, J. Jung, J. Jang, and J. C. Ye, “Wavelet minimum description length detrending for near-infrared spectroscopy,” J. Biomed. Opt. 14, 034004 (2009).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab. (1)

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. R. Stat. Soc. Ser B (Methodl.) (1)

Y. Benjamini and Y. Hochberg, “Controlling the flase discovery rate: a practical and powerful approach to multiple testing,” J. R. Stat. Soc. Ser B (Methodl.) 57, 289–300 (1995).

Magnetic Resonance Imaging (1)

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: Combined fMRI-fNIRS studies,” Magnetic Resonance Imaging 24, 495–505 (2006).
[CrossRef] [PubMed]

Nature Medicine (1)

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nature Medicine 9, 123–128 (2003).
[CrossRef] [PubMed]

NeuroImage (9)

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).
[CrossRef]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. S, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).
[CrossRef] [PubMed]

C. Genovese, N. Lazar, and T. Nichols, “Thresholding of statistical maps in functional neuroimaging using the false discovery rate,” NeuroImage 15, 870–878 (2002).
[CrossRef] [PubMed]

A. Singh and I. Dan, “Exploring the false discovery rate in multichannel NIRS,” NeuroImage 33, 542–549 (2006).
[CrossRef] [PubMed]

K. J. Friston, O. Josephs, E. Zarahn, A. P. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? bias and efficiency in fmri time-series analysis,” NeuroImage 12, 196–208 (2000).
[CrossRef] [PubMed]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: Statistical parametric mapping for near-infrared spectroscopy,” NeuroImage 44, 428–447 (2009).
[CrossRef]

T. Takahashi, Y. Takikawa, R. Kawagoe, S. Shibuya, T. Iwano, and S. Kitazawa, “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).
[CrossRef] [PubMed]

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. Eric, L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (3)

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, and S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Y. Zhang, D. H. Brooks, and D. A. Boas, “A haemodynamic response function model in spatio-temporal diffuse optical tomography,” Phys. Med. Biol. 50, 4625–4644 (2005).
[CrossRef] [PubMed]

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43, 2465–2478 (1998).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci. USA (1)

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Nat. Acad. Sci. USA 104, 12169–12174 (2007).
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[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Block-sparse MMV model when HbO and HbR are assumed to be correlated with each other. The shaded areas describe the index of simultaneously activated voxels of HbO and HbR, respectively.

Fig. 2
Fig. 2

Singular value distribution: each singular value is included in either signal subspace or noise subspace. The number of singular values in signal subspace is equal to the dimension of signal subspace.

Fig. 3
Fig. 3

Example of MUSIC spectrum for HbO; dimension of signal subspace is (a) one, (b) three (c) five. The spectrum distribution depends on the signal subspace dimension.

Fig. 4
Fig. 4

(a) Simulation setup for synthetic data, (b) synthetic ΔCHbO(red) and ΔCHbR(blue) at the activation area, and (c) locations of synthetic activation area on the horizontal plane. The big arrow in (a) indicates the activation placed in the middle position of the most lateral line in (c).

Fig. 5
Fig. 5

Block paradigm of RFT experiment.

Fig. 6
Fig. 6

Displacement error [mm] in lateral and depth directions when the activation changes along the lateral direction as shown in Fig. 4(c). The depth is fixed to (a) 30mm, (b) 44mm, respectively. (c) Lateral distance error averaged over depth.

Fig. 7
Fig. 7

Activation area for HbO using MUSIC (q < 0.05, corrected. df=2). The cross hair in coronal, sagittal and horizontal section indicates the position of the peak value of MUSIC spectrum.

Fig. 8
Fig. 8

Activation maps obtained from the right finger tapping task (Subject 1). MUSIC spectrum of DOT is based on combination of HbO and HbR, in which df = 1, q-level for FDR control is given as 0.01. fMRI images is controlled by p < 0.01 (corrected). (a) 3D rendering of the activation map for DOT (blue), fMRI (yellow-green), and intersectional area (red). (b) 2D maps for DOT with coronal, sagittal, and horizontal views.

Fig. 9
Fig. 9

Activation maps obtained from the right finger tapping task (Subject 3). MUSIC spectrum of DOT is based on combination of HbO and HbR, in which df = 1, q-level for FDR control is given as 0.01. fMRI images is controlled by p < 0.01 (corrected). (a) 3D rendering of the activation map for DOT (blue), fMRI (yellow-green), and intersectional area (red). (b) 2D maps for DOT with coronal, sagittal, and horizontal views.

Fig. 10
Fig. 10

COM positions of fMRI, νHbO, νHbR, and νHbO&HbR.

Tables (6)

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Table 1 Voxel classification in multiple testing of N hypotheses.

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Table 2 The wavelength-dependent optical properties of the segmented head model (absorption coefficient μa and reduced scattering coefficient μs) [4146].

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Table 3 Minimum distance between the MNI coordinate of left primary motor cortex (BA4) or somato-sensory cortex (BA123) and the COM of (a) fMRI, (b)–(d) MUSIC spectra from HbO, HbR, combination of HbO and HbR, respectively; the degrees of freedom for MUSIC spectrum for each individual case was set as two in (b), (c), and as four in (d). In group analysis, each df was tripled, thereby six for (b), (c), and twelve for (d).

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Table 4 The number of significant voxels in fMRI or DOT (HbO, HbR, HbO&HbR) and the number of voxels which are located within BA4 or BA123 among the total significant voxels in each fMRI and DOT method.

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Table 5 Displacement of the center of mass between fMRI and DOT using MUSIC spectra of (a) HbO, (b) HbR, and (c) HbO&HbR.

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Table 6 Depth and lateral displacement of the center of mass between fMRI and DOT using MUSIC spectra of (a) HbO, (b) HbR, and (c) HbO&HbR.

Equations (24)

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Δ ϕ ( r d , r s ; λ , t ) = ln U ( r d , r s ; λ , t ) U 0 ( r d , r s ; λ ) U 0 ( r d , r ; λ ) U 0 ( r , r s ; λ ) U 0 ( r d , r s ; λ ) Δ μ a ( r ; λ , t ) d r ,
y j λ = A λ u j λ + w j λ , j = 1 , 2 , , J ,
y j λ = [ Δ ϕ ( r d 1 , r s 1 ; λ , t j ) , Δ ϕ ( r d 2 , r s 2 ; λ , t j ) , , Δ ϕ ( r d m , r s m ; λ , t j ) ] T m , u j λ = [ Δ μ a ( r 1 ; λ , t j ) , Δ μ a ( r 2 ; λ , t j ) , , Δ μ a ( r n ; λ , t j ) ] T n ,
A i j λ = U 0 ( r d i , r j ; λ ) U 0 ( r j , r s i ; λ ) U 0 ( r d i , r s i ; λ ) δ ,
Δ μ a ( r ; λ , t ) = ɛ H b O λ Δ c H b O ( r ; t ) + ɛ H b R λ Δ c H b R ( r ; t ) ,
[ y j λ 1 y j λ 2 ] = A [ x H b O , j x H b R , j ] + [ w j λ 1 w j λ 2 ] ,
A = [ A H b O A H b R ] = [ ɛ H b O λ 1 A λ 1 ɛ H b R λ 1 A λ 1 ɛ H b O λ 2 A λ 2 ɛ H b R λ 2 A λ 2 ] ,
x H b O , j = [ Δ c H b O ( r 1 ; t j ) , Δ c H b O ( r 2 ; t j ) , , Δ c H b O ( r n ; t j ) ] T n ,
x H b R , j = [ Δ c H b R ( r 1 ; t j ) , Δ c H b R ( r 2 ; t j ) , , Δ c H b R ( r n ; t j ) ] T n .
Y = [ Y λ 1 Y λ 2 ] = A [ X H b O X H b R ] + [ W λ 1 W λ 2 ] = A X + W , A 2 m × 2 n , X 2 n × J
ν ( j ) = m U s H a j 2 2 .
ν ( i ) = { m U s H a i 2 2 , i = 1 , , n : ν H b O m U s H a i 2 2 , i = n + 1 , , 2 n : ν H b R
ν ex ( i ) = ν ( i ) + ν ( n + i ) = m U s H [ a i a n + i ] F 2 , i = 1 , , n . : ν H b O & H b R
F D R = F P F P + T P = F P T 1 ,
E ( FDR ) n 0 n q q .
p i i q n , i = n , n 1 , , 1.
min X 0 subject to Y = A X ,
R ^ Y = 1 J Y Y T J A R ^ X A T + σ 2 I ,
A R ^ X A T = U S S U S T
S = [ σ 1 2 σ 2 2 σ k 2 ] k × k .
span ( U s ) = span ( A X ) = span ( A I k ) ,
U S H a j 2 2 = 1 ,
U n H a j 2 2 = 0.
ν ( j ) = m U S H a j 2 2 ,

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