## Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography |

Biomedical Optics Express, Vol. 3, Issue 5, pp. 943-957 (2012)

http://dx.doi.org/10.1364/BOE.3.000943

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### Abstract

Abstract: In diffuse optical tomography (DOT), researchers often face challenges to accurately recover the depth and size of the reconstructed objects. Recent development of the Depth Compensation Algorithm (DCA) solves the depth localization problem, but the reconstructed images commonly exhibit over-smoothed boundaries, leading to fuzzy images with low spatial resolution. While conventional DOT solves a linear inverse model by minimizing least squares errors using L2 norm regularization, L1 regularization promotes sparse solutions. The latter may be used to reduce the over-smoothing effect on reconstructed images. In this study, we combined DCA with L1 regularization, and also with L2 regularization, to examine which combined approach provided us with an improved spatial resolution and depth localization for DOT. Laboratory tissue phantoms were utilized for the measurement with a fiber-based and a camera-based DOT imaging system. The results from both systems showed that L1 regularization clearly outperformed L2 regularization in both spatial resolution and depth localization of DOT. An example of functional brain imaging taken from human *in vivo* measurements was further obtained to support the conclusion of the study.

© 2012 OSA

## 1. Introduction

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**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

3. T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. **73**(7), 076701 (2010). [CrossRef]

3. T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. **73**(7), 076701 (2010). [CrossRef]

2. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. **25**(12), 123010 (2009). [CrossRef]

3. T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. **73**(7), 076701 (2010). [CrossRef]

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**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

2. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. **25**(12), 123010 (2009). [CrossRef]

**73**(7), 076701 (2010). [CrossRef]

**73**(7), 076701 (2010). [CrossRef]

4. M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. **50**(12), 2837–2858 (2005). [CrossRef] [PubMed]

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**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

5. C. K. Lee, C. W. Sun, P. L. Lee, H. C. Lee, C. Yang, C. P. Jiang, Y. P. Tong, T. C. Yeh, and J. C. Hsieh, “Study of photon migration with various source-detector separations in near-infrared spectroscopic brain imaging based on three-dimensional Monte Carlo modeling,” Opt. Express **13**(21), 8339–8348 (2005). [CrossRef] [PubMed]

6. 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]

7. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. **38**(13), 2950–2961 (1999). [CrossRef] [PubMed]

8. J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. **28**(21), 2061–2063 (2003). [CrossRef] [PubMed]

**23**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

6. 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]

9. 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]

10. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. **58**(6), 1182–1195 (2007). [CrossRef] [PubMed]

11. N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express **15**(21), 13695–13708 (2007). [CrossRef] [PubMed]

11. N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express **15**(21), 13695–13708 (2007). [CrossRef] [PubMed]

12. M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express **18**(23), 23676–23690 (2010). [CrossRef] [PubMed]

## 2. Methods

### 2.1. Theory of DOT

**73**(7), 076701 (2010). [CrossRef]

**23**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

**23**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

**73**(7), 076701 (2010). [CrossRef]

_{φ(r,t)}is the light fluence rate given at point

*r*and time point

*t.*is the isotropic light source, and

_{S(r,t)}*c*is the speed of light in the medium or tissue.

*D*is the diffusion coefficient defined by the absorption coefficient,

_{μa}, and reduced scattering coefficient,

_{μs'}, written as

_{D=[3(μa+μs')]−1}. Then, light propagation distribution

_{φ(r,t)}in Eq. (1) can be solved for a semi-infinite medium with an extrapolated zero boundary condition when either a pulsed laser [14

14. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. **28**(12), 2331–2336 (1989). [CrossRef] [PubMed]

15. T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. **19**(4), 879–888 (1992). [CrossRef] [PubMed]

16. A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A **14**(1), 246–254 (1997). [CrossRef] [PubMed]

_{μa}and

_{μs'}of the heterogeneities are regarded as perturbations from those of the background medium [3

**73**(7), 076701 (2010). [CrossRef]

_{δμs'}= 0). With all given assumptions and conditions, the Rytov formulation leads to a matrix notation for functional brain imaging by DOT [1

**23**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

**73**(7), 076701 (2010). [CrossRef]

17. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. **15**(2), R41–R93 (1999). [CrossRef]

**are given by**

*y*_{yi=−logφ(rs,i,rd,i)φ0(rs,i,rd,i)},with

*r*and

_{s,i}*r*representing positions of source,

_{d},_{i}*s*, and detector,

*d,*respectively, for the

*i*th measurement; matrix elements of

**are**

*x*_{xj=δμa,j}, which signify the perturbation in absorption,

_{μa}, at the

*j*th voxel within the imaging medium. Matrix

**is the Jacobian or sensitivity matrix and can be derived from the photon diffusion equation, Eq. (1), using the Rytov approximation [13,17**

*A*17. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. **15**(2), R41–R93 (1999). [CrossRef]

_{φ0(rs,i, rj) }and

_{φ0(rj, rd,i)}represent the light fluence rate at point

*r*resulting from source,

_{j}*s*, and contributing to detector,

*d*, for the

*i*th measurement, under the background medium conditions.

**represents the vector of measured optical densities, as defined by -log(**

*y**φ/φ*), between all possible pairs of sources and detectors at the measurement boundary and has the size of NM × 1, where NM is the number of measurements (or all possible combined pairs between sources and detectors). Vector

_{0}**in Eq. (2) represents changes in absorption in the three dimensional (3D) image space and has the size of NV × 1, where NV is the number of total voxels in the 3D space. Matrix**

*x***has dimensions of the number of measurements by number of voxels, namely, NM × NV. Equivalently, Matrix**

*A***is often called sensitivity matrix since it reflects the measurement sensitivity to the perturbation heterogeneity within each voxel in the medium. Matrix**

*A***is also the linear transformation between the measurement space and the voxel-based image space. Based on Eq. (3), matrix**

*A***can be analytically calculated by solving the forward model of light diffusion equation, Eq. (1), with the extrapolated boundary conditions [18**

*A*18. R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A **11**(10), 2727–2741 (1994). [CrossRef] [PubMed]

15. T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. **19**(4), 879–888 (1992). [CrossRef] [PubMed]

### 2.2. Regularization methods for DOT

#### 2.2.1. Depth compensation method (DCA)

**[6**

*M*6. 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]

9. 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]

**in deeper layers. Unlike other SVR methods [7**

*A*7. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. **38**(13), 2950–2961 (1999). [CrossRef] [PubMed]

19. J. P. Culver, T. Durduran, D. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, “Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia,” J. Cereb. Blood Flow Metab. **23**(8), 911–924 (2003). [CrossRef] [PubMed]

**is introduced to directly compensate the sensitivity matrix**

*M***. While the comprehensive details on DCA can be found in [6**

*A***35**(3), 429–431 (2010). [CrossRef] [PubMed]

9. 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]

**is formed as**

*M*_{M(Ai)}represents the maximum singular values for measurement sensitivities within the particular layer

*i =*1,2,

*L*, which is decomposed from the forward matrix

**;**

*A**γ*is an adjustable power and varies between 0 and 3. Notice that the maximum singular values are arranged inversely with respect to the matrix

**, namely, by the order from the bottom to surface, providing the maximum counterbalance for the deepest layer and vice versa. According to the previous studies,**

*A**γ*= 1.2–1.6 is considered to be appropriate for high-quality DOT images to recover embedded objects in deep tissue. In this study, a medium γ value of 1.3 was used. The adjusted sensitivity matrix

**is defined as**

*A*^{#}

*A*^{#}*=*

*AM**;*the modified inverse problem is given by

#### 2.2.2. Combination of DCA with L2 regularization

**,**

*A***is also under-determined and ill-posed, because the number of measurements are usually much fewer than the number of voxels to be reconstructed, as given in Eq. (5) [17**

*A*^{#}17. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. **15**(2), R41–R93 (1999). [CrossRef]

*λ*>0 is the regularization parameter and

_{‖‖22}denotes L2 norm. Equation (6) has an analytical solution, which can be solved directly or iteratively [2

2. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. **25**(12), 123010 (2009). [CrossRef]

**73**(7), 076701 (2010). [CrossRef]

**is the identity matrix,**

*I**S*

_{max}is the maximum eigenvalue of

_{A#A#T}, and

*α*is usually set in the range of 10

^{−3}to 10

^{−1}to suppress the measurement noise and stabilize the solution. While L2 norm regularization is an effective means of achieving stable solutions for the inverse problem and increasing predictive performance, it doesn’t promote sparse, sharp-edge solutions.

#### 2.2.3. Combination of DCA with L1 regularization

10. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. **58**(6), 1182–1195 (2007). [CrossRef] [PubMed]

11. N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express **15**(21), 13695–13708 (2007). [CrossRef] [PubMed]

**15**(21), 13695–13708 (2007). [CrossRef] [PubMed]

12. M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express **18**(23), 23676–23690 (2010). [CrossRef] [PubMed]

_{‖‖1}denotes L1 norm. In general, Eq. (8) does not have any analytical solution; the quality of the regularized solution depends on the choice of the regularization parameter, which was often selected manually. Also, the quality of reconstructed images depends on the user’s judgment. Several automatic methods, such as L-curve method, generalized cross validation method, and Morozov disperency principle, all were reported in [20,21] for this particular task.

22. S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process **1**(4), 606–617 (2007). [CrossRef]

22. S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process **1**(4), 606–617 (2007). [CrossRef]

**is the modified sensitivity matrix or Jacobian after incorporating DCA into the objective function,**

*A*^{#}**is the measurement matrix with dimension of NM × 1, and λ is the regularization parameter. Equation (8) doesn’t have an analytical solution but can be transformed into a convex quadratic form, which can be solved by standard convex optimization methods, such as interior point methods [22**

*y*22. S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process **1**(4), 606–617 (2007). [CrossRef]

_{u∈Rn}provides constraints on

*x*. Next, adding logarithmic barrier penalties results in

*t*varies from 0 to ∞, Eq. (10) converges to an optimal point. Equation (10) reaches the optimal point by utilizing Newton’s steps,

*NS*, and searching directions by pre-conjugate gradient (PCG) method [23

_{Newton}23. M. Benzi, C. D. Meyer, and M. Tuma, “A sparse approximate inverse preconditioner for the conjugate gradient method,” SIAM J. Sci. Comput. **17**(5), 1135–1149 (1996). [CrossRef]

*NI*, and

_{PCG}*NT*have a significant impact on the reconstructed images.

_{Newton}#### 2.2.4. Implementation of combined DCA with L1 regularization

- (1) Generate
matrix from PMI (Photon Migration Imaging) toolbox [24*A*];24. “PMI Toolbox,” http://www.nmr.mgh.harvard.edu/PMI/resources/toolbox.htm.

- (2) Modify
matrix to generate the combined matrix of*A*=*A*^{#}according to DCA;*AM* - (3) For image reconstruction using L2 regularization, we utilized PMI toolbox [24];
24. “PMI Toolbox,” http://www.nmr.mgh.harvard.edu/PMI/resources/toolbox.htm.

- (4) For image reconstruction using L1 regularization, we utilized L1-LS toolbox [25].
25. “L1-ls Toolbox,” http://www.stanford.edu/~boyd/l1_ls/.

*L1-LS*function can be expressed as

**=**

*x**l1_ls*(

**,**

*A*^{#}**, λ,**

*y**NI*), where

_{PCG,}NS_{Newton}**is a vector of NV × 1 to cover the 3D image volume,**

*x***is again the measurement vector containing the observed data, and λ is the regularization parameter. The reason we chose utilizing**

*y**L1-LS*toolbox was that it has been developed, tested, and supported by its publication [22

**1**(4), 606–617 (2007). [CrossRef]

*λ*(2) the value of gamma, γ, for the weight matrix

**, (3) the number of iterations in PCG,**

*M**NI*, and (4) Newton’s steps,

_{PCG}*NS*. The optimal selection of these four parameters determined the final quality of reconstructed DOT images. Based on literature,

_{Newton}*λ*values of 0.1-0.01 were usually chosen, depending on experimental noise levels. Based on our own studies [6

**35**(3), 429–431 (2010). [CrossRef] [PubMed]

**15**(4), 046005 (2010). [CrossRef] [PubMed]

26. F. Tian, H. Niu, S. Khadka, Z. J. Lin, and H. Liu, “Algorithmic depth compensation improves quantification and noise suppression in functional diffuse optical tomography,” Biomed. Opt. Express **1**(2), 441–452 (2010). [CrossRef] [PubMed]

*NI*and

_{PCG}*NS*. In this study, we finally selected

_{Newton}*NI*and

_{PCG}*NS*to be 60 and 15, based on trial and error. The ranges used to choose appropriate values of

_{Newton}*NI*and

_{PCG}*NS*in the trials were set 20-100 and 10-20, with an increment of 10 and 1, respectively. Specifically, the volume ratio (VR) between the reconstructed and actual objects was calculated for all the trials. A VR of unity served as a good performance criterion since VR was ideally expected to be close to “1”. In this way, the selected values of

_{Newton}*NI*= 60 and

_{PCG}*NS*= 15 provided us with an optimal VR in our current phantom study. Note that while running the trials to determine optimal values for

_{Newton}*NI*and

_{PCG}*NS*, we fixed values of

_{Newton}**and γ to be 0.01 and 1.3, respectively.**

*λ*### 2.3. Tissue phantom experiments

27. F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. **48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

28. Z. J. Lin, H. Niu, L. Li, and H. Liu, “Volumetric diffuse optical tomography for small animals using a CCD-camera-based imaging system,” Int. J. Opt. **2012**, 276367 (2012). [CrossRef]

27. F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. **48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

29. Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. **11**(6), 064019 (2006). [CrossRef] [PubMed]

30. X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. **43**(5), 1053–1062 (2004). [CrossRef] [PubMed]

#### 2.3.1. Fiber-based DOT imager

31. C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. **73**(2), 429 (2002). [CrossRef]

^{3}with 1% Intralipid solution. This solution served as the homogeneous background medium with an absorption coefficient (

*µ*) of 0.08 cm

_{a}^{−1}and reduced scattering coefficient (

_{μs'}) of 8.8 cm

^{−1}. Two spherical absorbers (

*µ*= 0.3 cm

_{a}^{−1}) of 1-cm diameter were placed at 3-cm depth around the center of optode array from the surface of container and separated by 3 cm, as shown in Fig. 1(a).

^{3}. After reconstruction, the resultant images were sliced along both lateral cross section and depth cross section separately to show the locations of the absorbers. The dotted lines in Fig. 1(a) outline the slices of both lateral (XY plane at Z = −3) and vertical cross section (XZ plane). All reconstructed images were normalized between 0 and 1 for comparison.

#### 2.3.2. Camera-based DOT imager

32. X. Cheng and D. Boas, “Diffuse optical reflection tomography using continuous wave illumination,” Opt. Express **3**(3), 118–123 (1998). [CrossRef] [PubMed]

33. L. Zhou, B. Yazıcı, A. B. Ale, and V. Ntziachristos, “Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data,” Opt. Lett. **35**(22), 3727–3729 (2010). [CrossRef] [PubMed]

*μ*= 0.1 cm

_{a}^{−1}and

_{μs'}= 10 cm

^{−1}. Two spherical absorbers of 8-mm in diameter were embedded at a depth of 2 cm below the liquid surface and separated by 2.5 cm; the two absorbers had a 3:1 contrast ratio in absorption between the absorbers and background.

^{3}, being the same as that in the fiber-based imaging case. Then, we sliced reconstructed images along lateral cross section (XY-plane at Z = −2mm) and depth cross section (XZ plane) to show the locations of the reconstructed absorbers. Reconstructed images were normalized between 0 and 1 for comparison.

#### 2.3.3. Measurement metrics

27. F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. **48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

28. Z. J. Lin, H. Niu, L. Li, and H. Liu, “Volumetric diffuse optical tomography for small animals using a CCD-camera-based imaging system,” Int. J. Opt. **2012**, 276367 (2012). [CrossRef]

**48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

29. Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. **11**(6), 064019 (2006). [CrossRef] [PubMed]

30. X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. **43**(5), 1053–1062 (2004). [CrossRef] [PubMed]

*µ*values are above 50% of the maximum

_{a}*µ*in the reconstructed image.

_{a}*w*and

_{VOI}*w*are the weight factor of the VOI and VOB relative to the entire volume (i.e., VOI or VOB divided by the entire volume),

_{VOB}*μ*and

_{VOI}*μ*are the mean values of

_{VOB}*µ*in the object and background volumes in a 3D reconstructed image, and

_{a}*σ*and

_{VOI}*σ*are the standard deviations of the two regions. In general, a high-quality reconstructed image possesses a VR value close to 1 and a high CNR value.

_{VOB}### 2.4. Applications of DCA-L1 method for human brain in vivo measurements

*in vivo*measurements, as an example. Specifically, we chose to image the motor cortex with our DOT while having the human subject perform a motor task (i.e., finger-tapping task) as a brain stimulation protocol. The reason to choose the motor task for assessing DOT was that this protocol has been studied intensively with either single-channel or multichannel near infrared spectroscopy (NIRS) by many research groups over the last decade [34

34. D. R. Leff, F. Orihuela-Espina, C. E. Elwell, T. Athanasiou, D. T. Delpy, A. W. Darzi, and G. Z. Yang, “Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies,” Neuroimage **54**(4), 2922–2936 (2011). [CrossRef] [PubMed]

34. D. R. Leff, F. Orihuela-Espina, C. E. Elwell, T. Athanasiou, D. T. Delpy, A. W. Darzi, and G. Z. Yang, “Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies,” Neuroimage **54**(4), 2922–2936 (2011). [CrossRef] [PubMed]

35. F. Tian, M. R. Delgado, S. C. Dhamne, B. Khan, G. Alexandrakis, M. I. Romero, L. Smith, D. Reid, N. J. Clegg, and H. Liu, “Quantification of functional near infrared spectroscopy to assess cortical reorganization in children with cerebral palsy,” Opt. Express **18**(25), 25973–25986 (2010). [CrossRef] [PubMed]

36. M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. **11**(5), 054007 (2006). [CrossRef] [PubMed]

**23**(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]

**73**(7), 076701 (2010). [CrossRef]

^{2}on each lateral side of the subject’s head and provided a total of 28 nearest S-D channels at a nearest S-D distance of 3.0 cm, as marked in Fig. 3(b).

37. 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. Natl. Acad. Sci. U.S.A. **104**(29), 12169–12174 (2007). [CrossRef] [PubMed]

**48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

**48**(13), 2496–2504 (2009). [CrossRef] [PubMed]

*y*for Eq. (5). Reconstructed hemodynamic images of motor activation were obtained after following the steps given in Section 2.2 (more specifically in Section 2.2.4). The sensitivity matrix,

_{i}**, was generated assuming**

*A**μ*(background) = 0.1 cm

_{a}^{−1}and

_{μs'}(background) = 10 cm

^{−1}for both wavelengths. In the process of DOT image reconstruction, volumetric imaging space of 20.32 × 5.84 × 4 cm

^{3}was created with a voxel size of 0.2x0.2x0.1 mm

^{3}. The constructed images were sliced at 2.5-cm depth along the lateral cross section (i.e., in XY plane at Z = −2.5 cm) in order to compare the performance of L1 and L2 regularizations.

## 3. Results

### 3.1. Results from tissue phantom experiments

### 3.2. Results from functional human brain imaging

35. F. Tian, M. R. Delgado, S. C. Dhamne, B. Khan, G. Alexandrakis, M. I. Romero, L. Smith, D. Reid, N. J. Clegg, and H. Liu, “Quantification of functional near infrared spectroscopy to assess cortical reorganization in children with cerebral palsy,” Opt. Express **18**(25), 25973–25986 (2010). [CrossRef] [PubMed]

*in vivo*human brain images.

## 4. Discussion and conclusion

**35**(3), 429–431 (2010). [CrossRef] [PubMed]

12. M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express **18**(23), 23676–23690 (2010). [CrossRef] [PubMed]

28. Z. J. Lin, H. Niu, L. Li, and H. Liu, “Volumetric diffuse optical tomography for small animals using a CCD-camera-based imaging system,” Int. J. Opt. **2012**, 276367 (2012). [CrossRef]

*in vivo*measurements. With DCA-L1, the reconstructed human brain images from a randomly selected human subject show significant improvement in depth localization and spatial resolution of the imaged activation region/volume in the brain. Specifically, reconstructed ΔHbO and ΔHbR changes derived from DCA-L1 are more localized and concentrated in the specific or expected region [see Figs. 6(a) and 6(b)], as compared to those resulting from DCA-L2 method. In contrast, the blurry effect of L2 regularization is clearly seen in reconstructed images [see Figs. 6(c) and 6(d)]. The reason that we believe DCA-L1 produces better DOT images in response to finger tapping is given as follows.

**15**(4), 046005 (2010). [CrossRef] [PubMed]

39. 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]

40. R. Parlapalli, V. Sharma, K. S. Gopinath, R. W. Briggs, and H. Liu, “Comparison of hemodynamic response non-linearity using simultaneous near infrared spectroscopy and magnetic resonance imaging modalities,” Proc. SPIE **7171**, 71710P, 71710P-12 (2009). [CrossRef]

37. 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. Natl. Acad. Sci. U.S.A. **104**(29), 12169–12174 (2007). [CrossRef] [PubMed]

41. B. Khan, P. Chand, and G. Alexandrakis, “Spatiotemporal relations of primary sensorimotor and secondary motor activation patterns mapped by NIR imaging,” Biomed. Opt. Express **2**(12), 3367–3386 (2011). [CrossRef] [PubMed]

34. D. R. Leff, F. Orihuela-Espina, C. E. Elwell, T. Athanasiou, D. T. Delpy, A. W. Darzi, and G. Z. Yang, “Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies,” Neuroimage **54**(4), 2922–2936 (2011). [CrossRef] [PubMed]

41. B. Khan, P. Chand, and G. Alexandrakis, “Spatiotemporal relations of primary sensorimotor and secondary motor activation patterns mapped by NIR imaging,” Biomed. Opt. Express **2**(12), 3367–3386 (2011). [CrossRef] [PubMed]

41. B. Khan, P. Chand, and G. Alexandrakis, “Spatiotemporal relations of primary sensorimotor and secondary motor activation patterns mapped by NIR imaging,” Biomed. Opt. Express **2**(12), 3367–3386 (2011). [CrossRef] [PubMed]

*NI*and

_{PCG}*NS*) were derived from our phantom results. For quantitative or rigorous validation of DCA-L1, we plan to conduct a joint fMRI-DOT study in order to make volumetric DOT possible for human brain imaging.

_{Newton}*in vivo*measurements of functional human brain imaging. In general, this DCA-L1 approach can be extended to other applications of DOT, such as breast and prostate cancer detection, and can be further explored to improve quantification of tumor optical properties because of more localized targets identified.

## Acknowledgments

## References and Links

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 |

2. | S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. |

3. | T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. |

4. | M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. |

5. | C. K. Lee, C. W. Sun, P. L. Lee, H. C. Lee, C. Yang, C. P. Jiang, Y. P. Tong, T. C. Yeh, and J. C. Hsieh, “Study of photon migration with various source-detector separations in near-infrared spectroscopic brain imaging based on three-dimensional Monte Carlo modeling,” Opt. Express |

6. | 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. |

7. | B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. |

8. | J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. |

9. | 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. |

10. | M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. |

11. | N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express |

12. | M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express |

13. | L. V. Wang and H. Wu, |

14. | M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. |

15. | T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. |

16. | A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A |

17. | S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. |

18. | R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A |

19. | J. P. Culver, T. Durduran, D. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, “Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia,” J. Cereb. Blood Flow Metab. |

20. | C. R. Vogel, |

21. | H. W. Engl, M. Hanke, and A. Neubauer, |

22. | S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process |

23. | M. Benzi, C. D. Meyer, and M. Tuma, “A sparse approximate inverse preconditioner for the conjugate gradient method,” SIAM J. Sci. Comput. |

24. | “PMI Toolbox,” http://www.nmr.mgh.harvard.edu/PMI/resources/toolbox.htm. |

25. | “L1-ls Toolbox,” http://www.stanford.edu/~boyd/l1_ls/. |

26. | F. Tian, H. Niu, S. Khadka, Z. J. Lin, and H. Liu, “Algorithmic depth compensation improves quantification and noise suppression in functional diffuse optical tomography,” Biomed. Opt. Express |

27. | F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. |

28. | Z. J. Lin, H. Niu, L. Li, and H. Liu, “Volumetric diffuse optical tomography for small animals using a CCD-camera-based imaging system,” Int. J. Opt. |

29. | Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. |

30. | X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. |

31. | C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. |

32. | X. Cheng and D. Boas, “Diffuse optical reflection tomography using continuous wave illumination,” Opt. Express |

33. | L. Zhou, B. Yazıcı, A. B. Ale, and V. Ntziachristos, “Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data,” Opt. Lett. |

34. | D. R. Leff, F. Orihuela-Espina, C. E. Elwell, T. Athanasiou, D. T. Delpy, A. W. Darzi, and G. Z. Yang, “Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies,” Neuroimage |

35. | F. Tian, M. R. Delgado, S. C. Dhamne, B. Khan, G. Alexandrakis, M. I. Romero, L. Smith, D. Reid, N. J. Clegg, and H. Liu, “Quantification of functional near infrared spectroscopy to assess cortical reorganization in children with cerebral palsy,” Opt. Express |

36. | M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. |

37. | 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. Natl. Acad. Sci. U.S.A. |

38. | Z. J. Lin, H. Niu, and H. Liu, “Feasibility study of volumetric diffuse optical tomography in small animal using CCD-camera-based imaging system,” OSA Technical Digest (CD) (Optical Society of America, 2010), paper BSuD108. |

39. | 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. |

40. | R. Parlapalli, V. Sharma, K. S. Gopinath, R. W. Briggs, and H. Liu, “Comparison of hemodynamic response non-linearity using simultaneous near infrared spectroscopy and magnetic resonance imaging modalities,” Proc. SPIE |

41. | B. Khan, P. Chand, and G. Alexandrakis, “Spatiotemporal relations of primary sensorimotor and secondary motor activation patterns mapped by NIR imaging,” Biomed. Opt. Express |

**OCIS Codes**

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.6960) Medical optics and biotechnology : Tomography

**ToC Category:**

Image Reconstruction and Inverse Problems

**History**

Original Manuscript: January 6, 2012

Revised Manuscript: April 5, 2012

Manuscript Accepted: April 5, 2012

Published: April 12, 2012

**Citation**

Venkaiah C. Kavuri, Zi-Jing Lin, Fenghua Tian, and Hanli Liu, "Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography," Biomed. Opt. Express **3**, 943-957 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-5-943

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### References

- D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage23(Suppl 1), S275–S288 (2004). [CrossRef] [PubMed]
- S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(12), 123010 (2009). [CrossRef]
- T. Durduran, R. Choe, W. Baker, and A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73(7), 076701 (2010). [CrossRef]
- M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol.50(12), 2837–2858 (2005). [CrossRef] [PubMed]
- C. K. Lee, C. W. Sun, P. L. Lee, H. C. Lee, C. Yang, C. P. Jiang, Y. P. Tong, T. C. Yeh, and J. C. Hsieh, “Study of photon migration with various source-detector separations in near-infrared spectroscopic brain imaging based on three-dimensional Monte Carlo modeling,” Opt. Express13(21), 8339–8348 (2005). [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]
- B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt.38(13), 2950–2961 (1999). [CrossRef] [PubMed]
- J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett.28(21), 2061–2063 (2003). [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]
- M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007). [CrossRef] [PubMed]
- N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express15(21), 13695–13708 (2007). [CrossRef] [PubMed]
- M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express18(23), 23676–23690 (2010). [CrossRef] [PubMed]
- L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley-Interscience, 2007).
- M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt.28(12), 2331–2336 (1989). [CrossRef] [PubMed]
- T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–888 (1992). [CrossRef] [PubMed]
- A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A14(1), 246–254 (1997). [CrossRef] [PubMed]
- S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15(2), R41–R93 (1999). [CrossRef]
- R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A11(10), 2727–2741 (1994). [CrossRef] [PubMed]
- J. P. Culver, T. Durduran, D. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, “Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia,” J. Cereb. Blood Flow Metab.23(8), 911–924 (2003). [CrossRef] [PubMed]
- C. R. Vogel, Computational Methods for Inverse Problems (Society for Industrial and Applied Mathematics, 2002).
- H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, 2000).
- S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process1(4), 606–617 (2007). [CrossRef]
- M. Benzi, C. D. Meyer, and M. Tuma, “A sparse approximate inverse preconditioner for the conjugate gradient method,” SIAM J. Sci. Comput.17(5), 1135–1149 (1996). [CrossRef]
- “PMI Toolbox,” http://www.nmr.mgh.harvard.edu/PMI/resources/toolbox.htm .
- “L1-ls Toolbox,” http://www.stanford.edu/~boyd/l1_ls/ .
- F. Tian, H. Niu, S. Khadka, Z. J. Lin, and H. Liu, “Algorithmic depth compensation improves quantification and noise suppression in functional diffuse optical tomography,” Biomed. Opt. Express1(2), 441–452 (2010). [CrossRef] [PubMed]
- F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt.48(13), 2496–2504 (2009). [CrossRef] [PubMed]
- Z. J. Lin, H. Niu, L. Li, and H. Liu, “Volumetric diffuse optical tomography for small animals using a CCD-camera-based imaging system,” Int. J. Opt.2012, 276367 (2012). [CrossRef]
- Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt.11(6), 064019 (2006). [CrossRef] [PubMed]
- X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt.43(5), 1053–1062 (2004). [CrossRef] [PubMed]
- C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum.73(2), 429 (2002). [CrossRef]
- X. Cheng and D. Boas, “Diffuse optical reflection tomography using continuous wave illumination,” Opt. Express3(3), 118–123 (1998). [CrossRef] [PubMed]
- L. Zhou, B. Yazıcı, A. B. Ale, and V. Ntziachristos, “Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data,” Opt. Lett.35(22), 3727–3729 (2010). [CrossRef] [PubMed]
- D. R. Leff, F. Orihuela-Espina, C. E. Elwell, T. Athanasiou, D. T. Delpy, A. W. Darzi, and G. Z. Yang, “Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies,” Neuroimage54(4), 2922–2936 (2011). [CrossRef] [PubMed]
- F. Tian, M. R. Delgado, S. C. Dhamne, B. Khan, G. Alexandrakis, M. I. Romero, L. Smith, D. Reid, N. J. Clegg, and H. Liu, “Quantification of functional near infrared spectroscopy to assess cortical reorganization in children with cerebral palsy,” Opt. Express18(25), 25973–25986 (2010). [CrossRef] [PubMed]
- M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt.11(5), 054007 (2006). [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. Natl. Acad. Sci. U.S.A.104(29), 12169–12174 (2007). [CrossRef] [PubMed]
- Z. J. Lin, H. Niu, and H. Liu, “Feasibility study of volumetric diffuse optical tomography in small animal using CCD-camera-based imaging system,” OSA Technical Digest (CD) (Optical Society of America, 2010), paper BSuD108.
- 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]
- R. Parlapalli, V. Sharma, K. S. Gopinath, R. W. Briggs, and H. Liu, “Comparison of hemodynamic response non-linearity using simultaneous near infrared spectroscopy and magnetic resonance imaging modalities,” Proc. SPIE7171, 71710P, 71710P-12 (2009). [CrossRef]
- B. Khan, P. Chand, and G. Alexandrakis, “Spatiotemporal relations of primary sensorimotor and secondary motor activation patterns mapped by NIR imaging,” Biomed. Opt. Express2(12), 3367–3386 (2011). [CrossRef] [PubMed]

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