Abstract

The paper presents a functional near-infrared spectroscopy (fNIRS)-based bundled-optode method for detection of the changes of oxy-hemoglobin (HbO) and deoxy-hemoglobin (HbR) concentrations. fNIRS with 32 optodes is utilized to measure five healthy male subjects’ brain-hemodynamic responses to arithmetic tasks. Specifically, the coordinates of 256 voxels in the three-dimensional (3D) volume are computed according to the known probe geometry. The mean path length factor in the Beer-Lambert equation is estimated as a function of the emitter-detector distance, which is utilized for computation of the absorption coefficient. The mean values of HbO and HbR obtained from the absorption coefficient are then applied for construction of a 3D fNIRS image. Our results show that the proposed method, as compared with the conventional approach, can detect brain activity with higher spatial resolution. This method can be extended for 3D fNIRS imaging in real-time applications.

© 2016 Optical Society of America

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    [Crossref] [PubMed]

2016 (3)

K.-S. Hong and N. Naseer, “Reduction of delay in detecting initial dips from functional near-infrared spectroscopy signals using vector-based phase analysis,” Int. J. Neural Syst. 26(3), 1650012 (2016).
[Crossref] [PubMed]

E. Miyashita and Y. Sakaguchi, “State variables of the arm may be encoded by single neuron activity in the monkey motor cortex,” IEEE Trans. Ind. Electron. 63(3), 1943–1952 (2016).
[Crossref]

K.-S. Hong and H. Santosa, “Decoding four different sound-categories in the auditory cortex using functional near-infrared spectroscopy,” Hear. Res. 333, 157–166 (2016).
[Crossref] [PubMed]

2015 (5)

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

M. J. Khan and K.-S. Hong, “Passive BCI based on drowsiness detection: an fNIRS study,” Biomed. Opt. Express 6(10), 4063–4078 (2015).
[Crossref] [PubMed]

K.-S. Hong, N. Naseer, and Y.-H. Kim, “Classification of prefrontal and motor cortex signals for three-class fNIRS-BCI,” Neurosci. Lett. 587, 87–92 (2015).
[Crossref] [PubMed]

O. Lee, S. Tak, and J. C. Ye, “A unified sparse recovery and inference framework for functional diffuse optical tomography using random effect model,” IEEE Trans. Med. Imaging 34(7), 1602–1615 (2015).
[Crossref] [PubMed]

M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
[Crossref] [PubMed]

2014 (12)

M. A. Kamran and K.-S. Hong, “Reduction of physiological effects in fNIRS waveforms for efficient brain-state decoding,” Neurosci. Lett. 580, 130–136 (2014).
[Crossref] [PubMed]

Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
[Crossref] [PubMed]

F. Tian and H. Liu, “Depth-compensated diffuse optical tomography enhanced by general linear model analysis and an anatomical atlas of human head,” Neuroimage 85(Pt 1), 166–180 (2014).
[Crossref] [PubMed]

G. E. Strangman, Q. Zhang, and Z. Li, “Scalp and skull influence on near infrared photon propagation in the Colin27 brain template,” Neuroimage 85(Pt 1), 136–149 (2014).
[Crossref] [PubMed]

M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
[Crossref] [PubMed]

M. J. Khan, M. J. Hong, and K.-S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci. 8, 244 (2014).
[Crossref] [PubMed]

N. Naseer, M. J. Hong, and K.-S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res. 232(2), 555–564 (2014).
[Crossref] [PubMed]

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
[Crossref] [PubMed]

K.-S. Hong and H.-D. Nguyen, “State-space models of impulse hemodynamic responses over motor, somatosensory, and visual cortices,” Biomed. Opt. Express 5(6), 1778–1798 (2014).
[Crossref] [PubMed]

F. Scholkmann, A. J. Metz, and M. Wolf, “Measuring tissue hemodynamics and oxygenation by continuous-wave functional near-infrared spectroscopy--how robust are the different calculation methods against movement artifacts?” Physiol. Meas. 35(4), 717–734 (2014).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, and K.-S. Hong, “Lateralization of music processing with noises in the auditory cortex: an fNIRS study,” Front. Behav. Neurosci. 8, 418 (2014).
[Crossref] [PubMed]

L. Gagnon, M. A. Yücel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” Neuroimage 85(Pt 1), 127–135 (2014).
[Crossref] [PubMed]

2013 (8)

S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
[Crossref] [PubMed]

N. A. Parks, “Concurrent application of TMS and near-infrared optical imaging: Methodological considerations and potential artifacts,” Front. Hum. Neurosci. 7, 592 (2013).
[Crossref] [PubMed]

M. Rehan and K.-S. Hong, “Modeling and automatic feedback control of tremor: adaptive estimation of deep brain stimulation,” PLoS One 8(4), e62888 (2013).
[Crossref] [PubMed]

M. A. Kamran and K.-S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng. 10(5), 056002 (2013).
[Crossref] [PubMed]

G. E. Strangman, Z. Li, and Q. Zhang, “Depth sensitivity and source-detector separations for near infrared spectroscopy based on the Colin27 brain template,” PLoS One 8(8), e66319 (2013).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, S.-P. Kim, and K.-S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum. 84(7), 073106 (2013).
[Crossref] [PubMed]

J.-K. Choi, M.-G. Choi, J.-M. Kim, and H.-M. Bae, “Efficient data extraction method for near-infrared spectroscopy (NIRS) systems with high spatial and temporal resolution,” IEEE Trans. Biomed. Circuits Syst. 7(2), 169–177 (2013).
[Crossref] [PubMed]

N. Naseer and K.-S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett. 553, 84–89 (2013).
[Crossref] [PubMed]

2012 (5)

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
[Crossref] [PubMed]

L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
[Crossref] [PubMed]

X. S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng. 9(2), 026012 (2012).
[Crossref] [PubMed]

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
[Crossref]

2011 (3)

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector Corrected Near Infrared Spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage 55(4), 1679–1685 (2011).
[Crossref] [PubMed]

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
[Crossref] [PubMed]

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

2010 (2)

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(4), 046005 (2010).
[Crossref] [PubMed]

H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[Crossref] [PubMed]

2009 (3)

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(10), D137–D143 (2009).
[Crossref] [PubMed]

C. Matteau-Pelletier, M. Dehaes, F. Lesage, and J.-M. Lina, “1/f noise in diffuse optical imaging and wavelet-based response estimation,” IEEE Trans. Med. Imaging 28(3), 415–422 (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(2), 428–447 (2009).
[Crossref] [PubMed]

2007 (3)

J. G. Kim and H. Liu, “Variation of haemoglobin extinction coefficients can cause errors in the determination of haemoglobin concentration measured by near-infrared spectroscopy,” Phys. Med. Biol. 52(20), 6295–6322 (2007).
[Crossref] [PubMed]

G. Taga, F. Homae, and H. Watanabe, “Effects of source-detector distance of near infrared spectroscopy on the measurement of the cortical hemodynamic response in infants,” Neuroimage 38(3), 452–460 (2007).
[Crossref] [PubMed]

Y. Hoshi, “Functional near-infrared spectroscopy: current status and future prospects,” J. Biomed. Opt. 12(6), 062106 (2007).
[Crossref] [PubMed]

2006 (1)

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

2004 (2)

2003 (3)

2002 (2)

H. L. Graber, Y. Pei, and R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21(8), 852–866 (2002).
[Crossref] [PubMed]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

1997 (1)

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[Crossref] [PubMed]

1993 (1)

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

1988 (1)

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref] [PubMed]

Ajichi, Y.

Alexandrakis, G.

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

Aqil, M.

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
[Crossref] [PubMed]

Arredondo, M. M.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Arridge, S.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref] [PubMed]

Arridge, S. R.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

Arthur, R. M.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
[Crossref]

Bae, H.-M.

J.-K. Choi, M.-G. Choi, J.-M. Kim, and H.-M. Bae, “Efficient data extraction method for near-infrared spectroscopy (NIRS) systems with high spatial and temporal resolution,” IEEE Trans. Biomed. Circuits Syst. 7(2), 169–177 (2013).
[Crossref] [PubMed]

Barbour, R. L.

H. L. Graber, Y. Pei, and R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21(8), 852–866 (2002).
[Crossref] [PubMed]

Basso Moro, S.

S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
[Crossref] [PubMed]

Behbehani, K.

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

Berger, A. J.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector Corrected Near Infrared Spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage 55(4), 1679–1685 (2011).
[Crossref] [PubMed]

Bhutta, M. R.

M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
[Crossref] [PubMed]

M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
[Crossref] [PubMed]

Boas, D. A.

L. Gagnon, M. A. Yücel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” Neuroimage 85(Pt 1), 127–135 (2014).
[Crossref] [PubMed]

L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
[Crossref] [PubMed]

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
[Crossref] [PubMed]

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

D. A. Boas, K. Chen, D. Grebert, and M. A. Franceschini, “Improving the diffuse optical imaging spatial resolution of the cerebral hemodynamic response to brain activation in humans,” Opt. Lett. 29(13), 1506–1508 (2004).
[Crossref] [PubMed]

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[Crossref] [PubMed]

Cazzell, M.

Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
[Crossref] [PubMed]

Chance, B.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[Crossref] [PubMed]

Chen, K.

Choi, J.-K.

J.-K. Choi, M.-G. Choi, J.-M. Kim, and H.-M. Bae, “Efficient data extraction method for near-infrared spectroscopy (NIRS) systems with high spatial and temporal resolution,” IEEE Trans. Biomed. Circuits Syst. 7(2), 169–177 (2013).
[Crossref] [PubMed]

Choi, M.-G.

J.-K. Choi, M.-G. Choi, J.-M. Kim, and H.-M. Bae, “Efficient data extraction method for near-infrared spectroscopy (NIRS) systems with high spatial and temporal resolution,” IEEE Trans. Biomed. Circuits Syst. 7(2), 169–177 (2013).
[Crossref] [PubMed]

Confer, N.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Cooper, R. J.

L. Gagnon, M. A. Yücel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” Neuroimage 85(Pt 1), 127–135 (2014).
[Crossref] [PubMed]

L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
[Crossref] [PubMed]

Cope, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref] [PubMed]

Culver, J. P.

Cutini, S.

S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
[Crossref] [PubMed]

Dale, A. M.

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

DaSilva, A. F.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Dehaes, M.

C. Matteau-Pelletier, M. Dehaes, F. Lesage, and J.-M. Lina, “1/f noise in diffuse optical imaging and wavelet-based response estimation,” IEEE Trans. Med. Imaging 28(3), 415–422 (2009).
[Crossref] [PubMed]

Dehghani, H.

Delpy, D. T.

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(16), 2915–2922 (2003).
[Crossref] [PubMed]

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
[Crossref] [PubMed]

Dhamne, S.

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(4), 046005 (2010).
[Crossref] [PubMed]

Efimov, I. R.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
[Crossref]

Essenpreis, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

Ferrari, M.

S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
[Crossref] [PubMed]

Firbank, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

Franceschini, M. A.

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

D. A. Boas, K. Chen, D. Grebert, and M. A. Franceschini, “Improving the diffuse optical imaging spatial resolution of the cerebral hemodynamic response to brain activation in humans,” Opt. Lett. 29(13), 1506–1508 (2004).
[Crossref] [PubMed]

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[Crossref] [PubMed]

Fukui, Y.

Gagnon, L.

L. Gagnon, M. A. Yücel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” Neuroimage 85(Pt 1), 127–135 (2014).
[Crossref] [PubMed]

L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
[Crossref] [PubMed]

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
[Crossref] [PubMed]

Ge, S. S.

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
[Crossref] [PubMed]

X. S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng. 9(2), 026012 (2012).
[Crossref] [PubMed]

Goldenholz, D.

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
[Crossref] [PubMed]

Gomba, M.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Graber, H. L.

H. L. Graber, Y. Pei, and R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21(8), 852–866 (2002).
[Crossref] [PubMed]

Grebert, D.

Greve, D. N.

L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
[Crossref] [PubMed]

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
[Crossref] [PubMed]

Habermehl, C.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
[Crossref] [PubMed]

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

Hiraoka, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref] [PubMed]

Hoge, R. D.

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

Holboke, M. J.

Holtze, S.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
[Crossref] [PubMed]

Homae, F.

G. Taga, F. Homae, and H. Watanabe, “Effects of source-detector distance of near infrared spectroscopy on the measurement of the cortical hemodynamic response in infants,” Neuroimage 38(3), 452–460 (2007).
[Crossref] [PubMed]

Hong, K.-S.

K.-S. Hong and H. Santosa, “Decoding four different sound-categories in the auditory cortex using functional near-infrared spectroscopy,” Hear. Res. 333, 157–166 (2016).
[Crossref] [PubMed]

K.-S. Hong and N. Naseer, “Reduction of delay in detecting initial dips from functional near-infrared spectroscopy signals using vector-based phase analysis,” Int. J. Neural Syst. 26(3), 1650012 (2016).
[Crossref] [PubMed]

M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
[Crossref] [PubMed]

M. J. Khan and K.-S. Hong, “Passive BCI based on drowsiness detection: an fNIRS study,” Biomed. Opt. Express 6(10), 4063–4078 (2015).
[Crossref] [PubMed]

K.-S. Hong, N. Naseer, and Y.-H. Kim, “Classification of prefrontal and motor cortex signals for three-class fNIRS-BCI,” Neurosci. Lett. 587, 87–92 (2015).
[Crossref] [PubMed]

N. Naseer, M. J. Hong, and K.-S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res. 232(2), 555–564 (2014).
[Crossref] [PubMed]

M. J. Khan, M. J. Hong, and K.-S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci. 8, 244 (2014).
[Crossref] [PubMed]

M. A. Kamran and K.-S. Hong, “Reduction of physiological effects in fNIRS waveforms for efficient brain-state decoding,” Neurosci. Lett. 580, 130–136 (2014).
[Crossref] [PubMed]

K.-S. Hong and H.-D. Nguyen, “State-space models of impulse hemodynamic responses over motor, somatosensory, and visual cortices,” Biomed. Opt. Express 5(6), 1778–1798 (2014).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, and K.-S. Hong, “Lateralization of music processing with noises in the auditory cortex: an fNIRS study,” Front. Behav. Neurosci. 8, 418 (2014).
[Crossref] [PubMed]

M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
[Crossref] [PubMed]

M. Rehan and K.-S. Hong, “Modeling and automatic feedback control of tremor: adaptive estimation of deep brain stimulation,” PLoS One 8(4), e62888 (2013).
[Crossref] [PubMed]

N. Naseer and K.-S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett. 553, 84–89 (2013).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, S.-P. Kim, and K.-S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum. 84(7), 073106 (2013).
[Crossref] [PubMed]

M. A. Kamran and K.-S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng. 10(5), 056002 (2013).
[Crossref] [PubMed]

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
[Crossref] [PubMed]

X. S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng. 9(2), 026012 (2012).
[Crossref] [PubMed]

Hong, M. J.

M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
[Crossref] [PubMed]

M. J. Khan, M. J. Hong, and K.-S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci. 8, 244 (2014).
[Crossref] [PubMed]

N. Naseer, M. J. Hong, and K.-S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res. 232(2), 555–564 (2014).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, and K.-S. Hong, “Lateralization of music processing with noises in the auditory cortex: an fNIRS study,” Front. Behav. Neurosci. 8, 418 (2014).
[Crossref] [PubMed]

M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
[Crossref] [PubMed]

H. Santosa, M. J. Hong, S.-P. Kim, and K.-S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum. 84(7), 073106 (2013).
[Crossref] [PubMed]

Hoshi, Y.

Y. Hoshi, “Functional near-infrared spectroscopy: current status and future prospects,” J. Biomed. Opt. 12(6), 062106 (2007).
[Crossref] [PubMed]

Hu, X. S.

X. S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng. 9(2), 026012 (2012).
[Crossref] [PubMed]

Hu, X.-S.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Huppert, T. J.

T. J. Huppert, R. D. Hoge, A. M. Dale, M. A. Franceschini, and D. A. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt. 11(6), 064018 (2006).
[Crossref] [PubMed]

Jang, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[Crossref] [PubMed]

Jang, K. E.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[Crossref] [PubMed]

Jeong, M.-Y.

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
[Crossref] [PubMed]

Johnson, T. D.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Jung, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[Crossref] [PubMed]

Kamran, M. A.

M. A. Kamran and K.-S. Hong, “Reduction of physiological effects in fNIRS waveforms for efficient brain-state decoding,” Neurosci. Lett. 580, 130–136 (2014).
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M. A. Kamran and K.-S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng. 10(5), 056002 (2013).
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Kaskhedikar, G.

L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
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Khan, B.

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
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M. J. Khan and K.-S. Hong, “Passive BCI based on drowsiness detection: an fNIRS study,” Biomed. Opt. Express 6(10), 4063–4078 (2015).
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J. G. Kim and H. Liu, “Variation of haemoglobin extinction coefficients can cause errors in the determination of haemoglobin concentration measured by near-infrared spectroscopy,” Phys. Med. Biol. 52(20), 6295–6322 (2007).
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H. Santosa, M. J. Hong, S.-P. Kim, and K.-S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum. 84(7), 073106 (2013).
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M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
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K.-S. Hong, N. Naseer, and Y.-H. Kim, “Classification of prefrontal and motor cortex signals for three-class fNIRS-BCI,” Neurosci. Lett. 587, 87–92 (2015).
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M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
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F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
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A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
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C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
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Kohl-Bareis, M.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
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Kovelman, I.

X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Laughner, J. I.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
[Crossref]

Lee, O.

O. Lee, S. Tak, and J. C. Ye, “A unified sparse recovery and inference framework for functional diffuse optical tomography using random effect model,” IEEE Trans. Med. Imaging 34(7), 1602–1615 (2015).
[Crossref] [PubMed]

Lee, S.-H.

M. R. Bhutta, K.-S. Hong, B.-M. Kim, M. J. Hong, Y.-H. Kim, and S.-H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum. 85(2), 026111 (2014).
[Crossref] [PubMed]

Lesage, F.

C. Matteau-Pelletier, M. Dehaes, F. Lesage, and J.-M. Lina, “1/f noise in diffuse optical imaging and wavelet-based response estimation,” IEEE Trans. Med. Imaging 28(3), 415–422 (2009).
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Li, L.

Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
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Li, Z.

G. E. Strangman, Q. Zhang, and Z. Li, “Scalp and skull influence on near infrared photon propagation in the Colin27 brain template,” Neuroimage 85(Pt 1), 136–149 (2014).
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G. E. Strangman, Z. Li, and Q. Zhang, “Depth sensitivity and source-detector separations for near infrared spectroscopy based on the Colin27 brain template,” PLoS One 8(8), e66319 (2013).
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Liebert, A.

Lin, Z.-J.

Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
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H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
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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(4), 046005 (2010).
[Crossref] [PubMed]

Lina, J.-M.

C. Matteau-Pelletier, M. Dehaes, F. Lesage, and J.-M. Lina, “1/f noise in diffuse optical imaging and wavelet-based response estimation,” IEEE Trans. Med. Imaging 28(3), 415–422 (2009).
[Crossref] [PubMed]

Liu, H.

Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
[Crossref] [PubMed]

F. Tian and H. Liu, “Depth-compensated diffuse optical tomography enhanced by general linear model analysis and an anatomical atlas of human head,” Neuroimage 85(Pt 1), 166–180 (2014).
[Crossref] [PubMed]

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

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(4), 046005 (2010).
[Crossref] [PubMed]

H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[Crossref] [PubMed]

J. G. Kim and H. Liu, “Variation of haemoglobin extinction coefficients can cause errors in the determination of haemoglobin concentration measured by near-infrared spectroscopy,” Phys. Med. Biol. 52(20), 6295–6322 (2007).
[Crossref] [PubMed]

Macdonald, R.

Malak, J.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
[Crossref] [PubMed]

Mata Pavia, J.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
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C. Matteau-Pelletier, M. Dehaes, F. Lesage, and J.-M. Lina, “1/f noise in diffuse optical imaging and wavelet-based response estimation,” IEEE Trans. Med. Imaging 28(3), 415–422 (2009).
[Crossref] [PubMed]

Mehnert, J.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
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Metz, A. J.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
[Crossref] [PubMed]

F. Scholkmann, A. J. Metz, and M. Wolf, “Measuring tissue hemodynamics and oxygenation by continuous-wave functional near-infrared spectroscopy--how robust are the different calculation methods against movement artifacts?” Physiol. Meas. 35(4), 717–734 (2014).
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E. Miyashita and Y. Sakaguchi, “State variables of the arm may be encoded by single neuron activity in the monkey motor cortex,” IEEE Trans. Ind. Electron. 63(3), 1943–1952 (2016).
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Möller, M.

Naseer, N.

K.-S. Hong and N. Naseer, “Reduction of delay in detecting initial dips from functional near-infrared spectroscopy signals using vector-based phase analysis,” Int. J. Neural Syst. 26(3), 1650012 (2016).
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K.-S. Hong, N. Naseer, and Y.-H. Kim, “Classification of prefrontal and motor cortex signals for three-class fNIRS-BCI,” Neurosci. Lett. 587, 87–92 (2015).
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N. Naseer, M. J. Hong, and K.-S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res. 232(2), 555–564 (2014).
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N. Naseer and K.-S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett. 553, 84–89 (2013).
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J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
[Crossref]

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Niu, H.

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

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(4), 046005 (2010).
[Crossref] [PubMed]

H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[Crossref] [PubMed]

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Obrig, H.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
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A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: Intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
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M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
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L. Gagnon, K. Perdue, D. N. Greve, D. Goldenholz, G. Kaskhedikar, and D. A. Boas, “Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling,” Neuroimage 56(3), 1362–1371 (2011).
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L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
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S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
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M. Rehan and K.-S. Hong, “Modeling and automatic feedback control of tremor: adaptive estimation of deep brain stimulation,” PLoS One 8(4), e62888 (2013).
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Saager, R. B.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector Corrected Near Infrared Spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage 55(4), 1679–1685 (2011).
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Sakaguchi, Y.

E. Miyashita and Y. Sakaguchi, “State variables of the arm may be encoded by single neuron activity in the monkey motor cortex,” IEEE Trans. Ind. Electron. 63(3), 1943–1952 (2016).
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K.-S. Hong and H. Santosa, “Decoding four different sound-categories in the auditory cortex using functional near-infrared spectroscopy,” Hear. Res. 333, 157–166 (2016).
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H. Santosa, M. J. Hong, and K.-S. Hong, “Lateralization of music processing with noises in the auditory cortex: an fNIRS study,” Front. Behav. Neurosci. 8, 418 (2014).
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H. Santosa, M. J. Hong, S.-P. Kim, and K.-S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum. 84(7), 073106 (2013).
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Schmitz, C. H.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
[Crossref] [PubMed]

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F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
[Crossref] [PubMed]

F. Scholkmann, A. J. Metz, and M. Wolf, “Measuring tissue hemodynamics and oxygenation by continuous-wave functional near-infrared spectroscopy--how robust are the different calculation methods against movement artifacts?” Physiol. Meas. 35(4), 717–734 (2014).
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X.-S. Hu, M. M. Arredondo, M. Gomba, N. Confer, A. F. DaSilva, T. D. Johnson, M. Shalinsky, and I. Kovelman, “Comparison of motion correction techniques applied to functional near-infrared spectroscopy data from children,” J. Biomed. Opt. 20(12), 126003 (2015).
[Crossref] [PubMed]

Steinbrink, J.

C. Habermehl, S. Holtze, J. Steinbrink, S. P. Koch, H. Obrig, J. Mehnert, and C. H. Schmitz, “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” Neuroimage 59(4), 3201–3211 (2012).
[Crossref] [PubMed]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: Intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref] [PubMed]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
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Strangman, G.

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
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Strangman, G. E.

G. E. Strangman, Q. Zhang, and Z. Li, “Scalp and skull influence on near infrared photon propagation in the Colin27 brain template,” Neuroimage 85(Pt 1), 136–149 (2014).
[Crossref] [PubMed]

G. E. Strangman, Z. Li, and Q. Zhang, “Depth sensitivity and source-detector separations for near infrared spectroscopy based on the Colin27 brain template,” PLoS One 8(8), e66319 (2013).
[Crossref] [PubMed]

Sulkin, M. S.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart Circul. Physiol. 303(7), H753–H765 (2012).
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Taga, G.

G. Taga, F. Homae, and H. Watanabe, “Effects of source-detector distance of near infrared spectroscopy on the measurement of the cortical hemodynamic response in infants,” Neuroimage 38(3), 452–460 (2007).
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Tak, S.

O. Lee, S. Tak, and J. C. Ye, “A unified sparse recovery and inference framework for functional diffuse optical tomography using random effect model,” IEEE Trans. Med. Imaging 34(7), 1602–1615 (2015).
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J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[Crossref] [PubMed]

Telleri, N. L.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector Corrected Near Infrared Spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage 55(4), 1679–1685 (2011).
[Crossref] [PubMed]

Tian, F.

F. Tian and H. Liu, “Depth-compensated diffuse optical tomography enhanced by general linear model analysis and an anatomical atlas of human head,” Neuroimage 85(Pt 1), 166–180 (2014).
[Crossref] [PubMed]

F. Tian, H. Niu, B. Khan, G. Alexandrakis, K. Behbehani, and H. Liu, “Enhanced functional brain imaging by using adaptive filtering and a depth compensation algorithm in diffuse optical tomography,” IEEE Trans. Med. Imaging 30(6), 1239–1251 (2011).
[Crossref] [PubMed]

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(4), 046005 (2010).
[Crossref] [PubMed]

H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[Crossref] [PubMed]

Tizzard, A.

Uludag, K.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
[Crossref] [PubMed]

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S. Basso Moro, S. Cutini, M. L. Ursini, M. Ferrari, and V. Quaresima, “Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study,” Front. Hum. Neurosci. 7, 925 (2013).
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A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: Intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref] [PubMed]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, and A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7(3), 464–470 (2002).
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A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
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Wabnitz, H.

Watanabe, H.

G. Taga, F. Homae, and H. Watanabe, “Effects of source-detector distance of near infrared spectroscopy on the measurement of the cortical hemodynamic response in infants,” Neuroimage 38(3), 452–460 (2007).
[Crossref] [PubMed]

White, B. R.

Wolf, M.

F. Scholkmann, A. J. Metz, and M. Wolf, “Measuring tissue hemodynamics and oxygenation by continuous-wave functional near-infrared spectroscopy--how robust are the different calculation methods against movement artifacts?” Physiol. Meas. 35(4), 717–734 (2014).
[Crossref] [PubMed]

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
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Wolf, U.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
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D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
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D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33(12), 1433–1442 (1988).
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Ye, J. C.

O. Lee, S. Tak, and J. C. Ye, “A unified sparse recovery and inference framework for functional diffuse optical tomography using random effect model,” IEEE Trans. Med. Imaging 34(7), 1602–1615 (2015).
[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(2), 428–447 (2009).
[Crossref] [PubMed]

Yodh, A. G.

Yücel, M. A.

L. Gagnon, M. A. Yücel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” Neuroimage 85(Pt 1), 127–135 (2014).
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L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
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Zeff, B. W.

Zhang, Q.

G. E. Strangman, Q. Zhang, and Z. Li, “Scalp and skull influence on near infrared photon propagation in the Colin27 brain template,” Neuroimage 85(Pt 1), 136–149 (2014).
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G. E. Strangman, Z. Li, and Q. Zhang, “Depth sensitivity and source-detector separations for near infrared spectroscopy based on the Colin27 brain template,” PLoS One 8(8), e66319 (2013).
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Zimmermann, R.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. Mata Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85(Pt 1), 6–27 (2014).
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N. Naseer, M. J. Hong, and K.-S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res. 232(2), 555–564 (2014).
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Front. Behav. Neurosci. (1)

H. Santosa, M. J. Hong, and K.-S. Hong, “Lateralization of music processing with noises in the auditory cortex: an fNIRS study,” Front. Behav. Neurosci. 8, 418 (2014).
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M. J. Khan, M. J. Hong, and K.-S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci. 8, 244 (2014).
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Front. Psychol. (1)

M. R. Bhutta, M. J. Hong, Y. H. Kim, and K.-S. Hong, “Single-trial lie detection using a combined fNIRS-polygraph system,” Front. Psychol. 6, 709 (2015).
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K.-S. Hong and H. Santosa, “Decoding four different sound-categories in the auditory cortex using functional near-infrared spectroscopy,” Hear. Res. 333, 157–166 (2016).
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Z.-J. Lin, L. Li, M. Cazzell, and H. Liu, “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35(8), 4249–4266 (2014).
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IEEE Trans. Biomed. Circuits Syst. (1)

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J. Neural Eng. (2)

X. S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng. 9(2), 026012 (2012).
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Neuroimage (12)

M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage 63(1), 553–568 (2012).
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L. Gagnon, R. J. Cooper, M. A. Yücel, K. L. Perdue, D. N. Greve, and D. A. Boas, “Short separation channel location impacts the performance of short channel regression in NIRS,” Neuroimage 59(3), 2518–2528 (2012).
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Figures (10)

Fig. 1
Fig. 1

(a) Concept of bundled-optode configuration, (b) light traveling through tissues in banana-shaped light path, and (c) locations of channels in the 3D space (x, y, z) computed from a pair of an emitter (circle) and a detector (white square): Italic numbers indicate optode-positions.

Fig. 2
Fig. 2

Experimental paradigm for arithmetic tasks (repeated five times): For each trial, subjects are asked to answer to the displayed questions on a laptop screen within 10 s (i.e., gray bar) and to relax during the resting state.

Fig. 3
Fig. 3

An optode arrangement for identifying a local brain region activated from arithmetic tasks: Fp1 and Fp2 are two reference points in the international 10-20 system, circles and squares denote emitters and detectors, respectively, and numbers in red indicate channels.

Fig. 4
Fig. 4

A bundled-optode arrangement for acquisition of HRs in a local brain region.

Fig. 5
Fig. 5

The partial sensitivity (L) of GM (blue solid line) and WM (red dashed line) estimated as a function of distance.

Fig. 6
Fig. 6

Active brain regions of representative Subject 3 identified using the optode arrangement in Fig. 3: Numbers in white indicate the channels and the color bar on the right-hand side denotes the activation strength according to the mean values of HbOs.

Fig. 7
Fig. 7

An active (representative) channel (Ch. 234) of Subject 3 (blue and red thick curves represent unfiltered and filtered HbX, respectively) using the proposed method: (a) HbO, (c) HbR, (b) and (d) are HbO and HbR averaged across five trials from (a) and (c), respectively, and gray bars denote stimuli of arithmetic tasks (the boundaries in (b) and (d) denote one standard deviation).

Fig. 8
Fig. 8

Comparison of the active locations of two methods (3D brain imaging constructed from the mean values of HbOs of Subject 3): The conventional method ((a), (c), and (e)), the proposed method ((b), (d), and (f)), and the color bar at the bottom denotes the activation strength of the mean values of HbOs standardized in 0~1 range.

Fig. 9
Fig. 9

Comparison of the active locations of two methods (left view, Subject 1 (first row) and Subject 2 (second row): The conventional method (a, c) and the proposed method (b, d).

Fig. 10
Fig. 10

Comparison of active locations in two methods (left view, Subject 4 (first row) and Subject 5 (second row): The conventional method (a, c) and the proposed method (b, d).

Tables (1)

Tables Icon

Table 1 Comparison of the number of active channels in ROIs across 5 subjects

Equations (13)

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

I out (t,λ)= I in (t,λ) e μ a (t,λ)×L+G(λ) ,
O D i (t,λ)=ln I out i (t,λ) I in i (t,λ) = μ a i (t,λ)× L i +G(λ),
ΔO D i (t,λ)=ln I out i (t,λ) I out i (t1,λ) =Δ μ a i (t,λ)× L i .
Δ μ a i (t,λ)= ε HbO (λ)Δ C HbO i (t)+ ε HbR (λ)Δ C HbR i (t).
ΔO D i (t,λ) Δ μ a i (t,λ) = L i .
ΔO D i (t,λ)Δ μ a i,scalp (t,λ)× L i,scalp +Δ μ a i,skull (t,λ)× L i,skull + Δ μ a i,CSF (t,λ)× L i,CSF +Δ μ a i,GM (t,λ)× L i,GM + Δ μ a i,WM (t,λ)× L i,WM .
ΔO D i (t,λ)=Δ μ a i,GM (t,λ)× L i,GM +Δ μ a i,WM (t,λ)× L i,WM ( L i,GM + L i,WM )×Δ μ a i (t,λ).
[ ΔO D 1 (t,λ) ΔO D 2 (t,λ) ΔO D N (t,λ) ]=[ L 1,GM + L 1,WM 0 0 0 0 L 2,GM + L 2,WM 0 0 0 0 L N,GM + L N,WM ][ Δ μ a 1 (t,λ) Δ μ a 2 (t,λ) Δ μ a N (t,λ) ].
[ Δ μ a 1 (t, λ 1 ) Δ μ a 2 (t, λ 1 ) Δ μ a N (t, λ 1 ) ]= [ L 1,GM + L 1,WM 0 0 0 0 L 2,GM + L 2,WM 0 0 0 0 L N,GM + L N,WM ] 1 [ ΔO D 1 (t, λ 1 ) ΔO D 2 (t, λ 1 ) ΔO D N (t, λ 1 ) ],
[ Δ μ a 1 (t, λ 2 ) Δ μ a 2 (t, λ 2 ) Δ μ a N (t, λ 2 ) ]= [ L 1,GM + L 1,WM 0 0 0 0 L 2,GM + L 2,WM 0 0 0 0 L N,GM + L N,WM ] 1 [ ΔO D 1 (t, λ 2 ) ΔO D 2 (t, λ 2 ) ΔO D N (t, λ 2 ) ].
[ Δ C HbO i (t) Δ C HbR i (t) ]= [ ε HbO ( λ 1 ) ε HbR ( λ 1 ) ε HbO ( λ 2 ) ε HbR ( λ 2 ) ] 1 [ Δ μ a i (t, λ 1 ) Δ μ a i (t, λ 2 ) ].
L GM =1.2047×d17.8875,
L WM =0.1185×d1.9922,

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