Abstract

Spectrally constrained diffuse optical tomography (SCDOT) is known to improve reconstruction in diffuse optical imaging; constraining the reconstruction by coupling the optical properties across multiple wavelengths suppresses artefacts in the resulting reconstructed images. In other work, L1-norm regularization has been shown to improve certain types of image reconstruction problems as its sparsity-promoting properties render it robust against noise and enable the preservation of edges in images, but because the L1-norm is non-differentiable, it is not always simple to implement. In this work, we show how to incorporate L1 regularization into SCDOT. Three popular algorithms for L1 regularization are assessed for application in SCDOT: iteratively reweighted least square algorithm (IRLS), alternating directional method of multipliers (ADMM) and fast iterative shrinkage-thresholding algorithm (FISTA). We introduce an objective procedure for determining the regularization parameter in these algorithms and compare their performance in simulated experiments, and in real data acquired from a tissue phantom. Our results show that L1 regularization consistently outperforms Tikhonov regularization in this application, particularly in the presence of noise.

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2017 (1)

D. Lighter, A. Filer, and H. Dehghani, “Multispectral diffuse optical tomography of finger joints,” Proc. SPIE 10412, 104120N (2017).

2016 (5)

H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
[Crossref] [PubMed]

J. A. Guggenheim, I. Bargigia, A. Farina, A. Pifferi, and H. Dehghani, “Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery,” Biomed. Opt. Express 7(9), 3784–3794 (2016).
[Crossref] [PubMed]

W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
[Crossref]

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
[Crossref]

J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
[Crossref]

2015 (1)

J. Duan, Z. Pan, B. Zhang, W. Liu, and X. Tai, “Fast algorithm for color texture image inpainting using the non-local CTV model,” Journal of Global Optimization 62(4), 853–876 (2015).
[Crossref]

2014 (6)

M. Schweiger and S. Arridge, “The Toast++ software suite for forward and inverse modeling in optical tomography,” J. Biomed. Opt. 19(4), 040801 (2014).
[Crossref] [PubMed]

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
[Crossref]

J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
[Crossref]

A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
[Crossref] [PubMed]

C. B. Shaw and P. K. Yalavarthy, “Performance evaluation of typical approximation algorithms for nonconvex lp-minimization in diffuse optical tomography,” J. Opt. Soc. Am. A 31(4), 852–862 (2014).
[Crossref]

X. Wu, A. T. Eggebrecht, S. L. Ferradal, J. P. Culver, and H. Dehghani, “Quantitative evaluation of atlas-based high-density diffuse optical tomography for imaging of the human visual cortex,” Biomedical Optics Express 5(11), 3882–3900 (2014).
[Crossref] [PubMed]

2013 (3)

J. Prakash and P. K. Yalavarthy, “A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography,” Medical Physics 40(3), 033101 (2013).
[Crossref] [PubMed]

R. P. K. Jagannath and P. K. Yalavarthy, “Nonquadratic penalization improves near-infrared diffuse optical tomography,” J. Opt. Soc. Am. A 30(8), 1516–1523 (2013).
[Crossref]

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical lp minimization algorithms,” Neurocomputing 119, 413–424 (2013).
[Crossref]

2012 (5)

H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
[Crossref] [PubMed]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using L1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17(8), 0860091 (2012).
[Crossref]

V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3(5), 943–957 (2012).
[Crossref] [PubMed]

Y. Zhan, A. T. Eggebrecht, J. P. Culver, and H. Dehghani, “Singular value decomposition based regularization prior to spectral mixing improves crosstalk in dynamic imaging using spectral diffuse optical tomography,” Biomed. Opt. Express 3(9), 2036–2049 (2012).
[Crossref] [PubMed]

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

2011 (4)

S. Okawa, Y. Hoshi, and Y. Yamada, “Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization,” Biomed. Opt. Express 2(12), 3334–3348 (2011).
[Crossref] [PubMed]

J-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Transactions on Medical Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Transactions on Image Processing 20(3), 681–695 (2011).
[Crossref]

H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
[Crossref] [PubMed]

2010 (3)

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
[Crossref]

I. Daubechies, R. DeVore, M. Fornasier, and C. S. Güntürk, “Iteratively reweighted least squares minimization for sparse recovery,” Communications on Pure and Applied Mathematics 63(1), 1–38 (2010).
[Crossref]

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE Transactions on Image Processing 19(9), 2345–2356 (2010).
[Crossref] [PubMed]

2009 (5)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Journal on Imaging Sciences 2(1), 183–202 (2009).
[Crossref]

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Problems 25(12), 123010 (2009).
[Crossref]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

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]

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Transactions on Signal Processing 57(7), 2479–2493 (2009).
[Crossref]

2007 (3)

C. Vonesch and M. Unser, “A fast iterative thresholding algorithm for wavelet-regularized deconvolution,” Proc. SPIE 6701, 1–5 (2007).

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
[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,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
[Crossref]

2006 (2)

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution,” Communications on Pure and Applied Mathematics 59(6), 797–829 (2006).
[Crossref]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

2005 (5)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Physics in Medicine and Biology 50(4), R1–R43 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

X. Heng, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging–coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44(11), 2177–2188 (2005).
[Crossref]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

2004 (3)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on Pure and Applied Mathematics 57(11), 1413–1457 (2004).
[Crossref]

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

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,” Optics Letters 29(13), 1506–1508 (2004).
[Crossref] [PubMed]

2003 (7)

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
[Crossref] [PubMed]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
[Crossref] [PubMed]

M. A. T. Figueiredo and R. D. Nowak, “An Em algorithm for wavelet-based image restoration,” IEEE Transactions on Image Processing 12(8), 906–916 (2003).
[Crossref]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
[Crossref] [PubMed]

V. A. Markel, V. Mital, and J. C. Schotland, “Inverse problem in optical diffusion tomography. iii. inversion formulas and singular-value decomposition,” J. Opt. Soc. Am. A 20(5), 890–902 (2003).
[Crossref]

H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
[Crossref] [PubMed]

2001 (2)

V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. i. Fourier–Laplace inversion formulas,” J. Opt. Soc. Am. A 18(6), 1336–1347 (2001).
[Crossref]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
[Crossref]

2000 (1)

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, and A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61(4), 4295 (2000).
[Crossref]

1999 (1)

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

1998 (1)

A. Chambolle, R. A. De Vore, N-Y. Lee, and B. J. Lucier, “Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage,” IEEE Transactions on Image Processing 7(3), 319–335 (1998).
[Crossref]

1995 (2)

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: Finite-element-method calculations,” Appl. Opt. 34(34), 8026–8037 (1995).
[Crossref] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Medical Physics 22(11), 1779–1792 (1995).
[Crossref] [PubMed]

1970 (1)

B. Martinet, “Régularisation d’inéquations variationelles par approximations successives,” RIRO 4, 154–159 (1970).
[Crossref]

Afonso, M. V.

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Transactions on Image Processing 20(3), 681–695 (2011).
[Crossref]

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE Transactions on Image Processing 19(9), 2345–2356 (2010).
[Crossref] [PubMed]

Arridge, S.

M. Schweiger and S. Arridge, “The Toast++ software suite for forward and inverse modeling in optical tomography,” J. Biomed. Opt. 19(4), 040801 (2014).
[Crossref] [PubMed]

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Problems 25(12), 123010 (2009).
[Crossref]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Physics in Medicine and Biology 50(4), R1–R43 (2005).
[Crossref] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Medical Physics 22(11), 1779–1792 (1995).
[Crossref] [PubMed]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: Finite-element-method calculations,” Appl. Opt. 34(34), 8026–8037 (1995).
[Crossref] [PubMed]

Ashburner, J.

J. Ashburner and K. J. Friston, “Image segmentation,” in Human Brain Function2nd ed., R.S.J. Frackowiak, K.J. Friston, C. Frith, R. Dolan, K.J. Friston, C.J. Price, S. Zeki, J. Ashburner, and W.D. Penny, eds. (Academic, 2003).

Bai, L.

W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
[Crossref]

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
[Crossref]

J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
[Crossref]

Bargigia, I.

Baritaux, J-C.

J-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Transactions on Medical Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

Basevi, H. R. A.

H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
[Crossref] [PubMed]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Journal on Imaging Sciences 2(1), 183–202 (2009).
[Crossref]

Bioucas-Dias, J. M.

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Transactions on Image Processing 20(3), 681–695 (2011).
[Crossref]

M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE Transactions on Image Processing 19(9), 2345–2356 (2010).
[Crossref] [PubMed]

Boas, D. A.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
[Crossref]

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,” Optics Letters 29(13), 1506–1508 (2004).
[Crossref] [PubMed]

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

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
[Crossref]

Bresler, Y.

J. C. Ye, S. Y. Lee, and Y. Bresler, “Exact reconstruction formula for diffuse optical tomography using simultaneous sparse representation,” in 5th International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2008), pp. 1621–1624.

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
[Crossref]

Brooksby, B.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
[Crossref] [PubMed]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
[Crossref] [PubMed]

Bucher, M.

J-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Transactions on Medical Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
[Crossref] [PubMed]

Chambolle, A.

A. Chambolle, R. A. De Vore, N-Y. Lee, and B. J. Lucier, “Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage,” IEEE Transactions on Image Processing 7(3), 319–335 (1998).
[Crossref]

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
[Crossref] [PubMed]

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, and A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61(4), 4295 (2000).
[Crossref]

Chen, C.

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

Chen, K.

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,” Optics Letters 29(13), 1506–1508 (2004).
[Crossref] [PubMed]

Choe, R.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
[Crossref] [PubMed]

Culver, J. P.

X. Wu, A. T. Eggebrecht, S. L. Ferradal, J. P. Culver, and H. Dehghani, “Quantitative evaluation of atlas-based high-density diffuse optical tomography for imaging of the human visual cortex,” Biomedical Optics Express 5(11), 3882–3900 (2014).
[Crossref] [PubMed]

A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
[Crossref] [PubMed]

Y. Zhan, A. T. Eggebrecht, J. P. Culver, and H. Dehghani, “Singular value decomposition based regularization prior to spectral mixing improves crosstalk in dynamic imaging using spectral diffuse optical tomography,” Biomed. Opt. Express 3(9), 2036–2049 (2012).
[Crossref] [PubMed]

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48(10), D137–D143 (2009).
[Crossref] [PubMed]

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
[Crossref]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
[Crossref] [PubMed]

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, and A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61(4), 4295 (2000).
[Crossref]

Custo, A.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
[Crossref]

Dale, A. M.

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

Dan, I.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
[Crossref]

Daubechies, I.

I. Daubechies, R. DeVore, M. Fornasier, and C. S. Güntürk, “Iteratively reweighted least squares minimization for sparse recovery,” Communications on Pure and Applied Mathematics 63(1), 1–38 (2010).
[Crossref]

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on Pure and Applied Mathematics 57(11), 1413–1457 (2004).
[Crossref]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

De Mol, C.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on Pure and Applied Mathematics 57(11), 1413–1457 (2004).
[Crossref]

De Vore, R. A.

A. Chambolle, R. A. De Vore, N-Y. Lee, and B. J. Lucier, “Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage,” IEEE Transactions on Image Processing 7(3), 319–335 (1998).
[Crossref]

Defrise, M.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on Pure and Applied Mathematics 57(11), 1413–1457 (2004).
[Crossref]

Dehghani, H.

D. Lighter, A. Filer, and H. Dehghani, “Multispectral diffuse optical tomography of finger joints,” Proc. SPIE 10412, 104120N (2017).

H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
[Crossref] [PubMed]

J. A. Guggenheim, I. Bargigia, A. Farina, A. Pifferi, and H. Dehghani, “Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery,” Biomed. Opt. Express 7(9), 3784–3794 (2016).
[Crossref] [PubMed]

X. Wu, A. T. Eggebrecht, S. L. Ferradal, J. P. Culver, and H. Dehghani, “Quantitative evaluation of atlas-based high-density diffuse optical tomography for imaging of the human visual cortex,” Biomedical Optics Express 5(11), 3882–3900 (2014).
[Crossref] [PubMed]

A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
[Crossref] [PubMed]

H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
[Crossref] [PubMed]

Y. Zhan, A. T. Eggebrecht, J. P. Culver, and H. Dehghani, “Singular value decomposition based regularization prior to spectral mixing improves crosstalk in dynamic imaging using spectral diffuse optical tomography,” Biomed. Opt. Express 3(9), 2036–2049 (2012).
[Crossref] [PubMed]

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48(10), D137–D143 (2009).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

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,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
[Crossref]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
[Crossref] [PubMed]

X. Heng, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging–coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44(11), 2177–2188 (2005).
[Crossref]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
[Crossref] [PubMed]

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M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Medical Physics 22(11), 1779–1792 (1995).
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D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
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J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
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J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
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A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
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Ferradal, S. L.

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D. Lighter, A. Filer, and H. Dehghani, “Multispectral diffuse optical tomography of finger joints,” Proc. SPIE 10412, 104120N (2017).

H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
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D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
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J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
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I. Daubechies, R. DeVore, M. Fornasier, and C. S. Güntürk, “Iteratively reweighted least squares minimization for sparse recovery,” Communications on Pure and Applied Mathematics 63(1), 1–38 (2010).
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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 Transactions on Medical Imaging 18(3), 262–271 (1999).
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A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
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Hershey, T.

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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 Transactions on Medical Imaging 18(3), 262–271 (1999).
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M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Medical Physics 22(11), 1779–1792 (1995).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
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H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
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Jiang, S.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
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S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
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S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
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H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
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J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
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Kavuri, V. C.

Khadka, S.

H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
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Klose, A. D.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Transactions on Medical Imaging 18(3), 262–271 (1999).
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S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
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D. Kong and C. H. Q. Ding, “Non-convex feature learning via Lp,∞ operator,” In Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI Press, 2014) pp. 1918–1924.

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H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
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X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, and A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61(4), 4295 (2000).
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D. Lighter, A. Filer, and H. Dehghani, “Multispectral diffuse optical tomography of finger joints,” Proc. SPIE 10412, 104120N (2017).

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V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3(5), 943–957 (2012).
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V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3(5), 943–957 (2012).
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H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
[Crossref]

Liu, W.

J. Duan, Z. Pan, B. Zhang, W. Liu, and X. Tai, “Fast algorithm for color texture image inpainting using the non-local CTV model,” Journal of Global Optimization 62(4), 853–876 (2015).
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Lu, C.

H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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Lu, W.

W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
[Crossref]

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
[Crossref]

J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
[Crossref]

Lucier, B. J.

A. Chambolle, R. A. De Vore, N-Y. Lee, and B. J. Lucier, “Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage,” IEEE Transactions on Image Processing 7(3), 319–335 (1998).
[Crossref]

Lyu, Q.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical lp minimization algorithms,” Neurocomputing 119, 413–424 (2013).
[Crossref]

Manjappa, R.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
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[Crossref]

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
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Mital, V.

Niu, H.

H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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Nowak, R. D.

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Transactions on Signal Processing 57(7), 2479–2493 (2009).
[Crossref]

M. A. T. Figueiredo and R. D. Nowak, “An Em algorithm for wavelet-based image restoration,” IEEE Transactions on Image Processing 12(8), 906–916 (2003).
[Crossref]

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
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Okawa, S.

Pan, Z.

J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
[Crossref]

W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
[Crossref]

J. Duan, Z. Pan, B. Zhang, W. Liu, and X. Tai, “Fast algorithm for color texture image inpainting using the non-local CTV model,” Journal of Global Optimization 62(4), 853–876 (2015).
[Crossref]

J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
[Crossref]

Pattanayak, D. N.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, and A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61(4), 4295 (2000).
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B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
[Crossref] [PubMed]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

X. Heng, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging–coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44(11), 2177–2188 (2005).
[Crossref]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
[Crossref] [PubMed]

Pifferi, A.

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

X. Heng, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging–coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44(11), 2177–2188 (2005).
[Crossref]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
[Crossref] [PubMed]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
[Crossref] [PubMed]

Poplack, S. P.

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

Prakash, J.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
[Crossref]

J. Prakash and P. K. Yalavarthy, “A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography,” Medical Physics 40(3), 033101 (2013).
[Crossref] [PubMed]

Proudlock, F.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
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J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
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W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
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A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
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Samani, N. N.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
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J-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Transactions on Medical Imaging 30(5), 1143–1153 (2011).
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Schlaggar, B. L.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
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C. B. Shaw and P. K. Yalavarthy, “Performance evaluation of typical approximation algorithms for nonconvex lp-minimization in diffuse optical tomography,” J. Opt. Soc. Am. A 31(4), 852–862 (2014).
[Crossref]

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
[Crossref]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using L1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17(8), 0860091 (2012).
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Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical lp minimization algorithms,” Neurocomputing 119, 413–424 (2013).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
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A. T. Eggebrecht, S. L. Ferradal, A. Robichaux-Viehoever, M. S. Hassanpour, H. Dehghani, A. Z. Snyder, T. Hershey, and J. P. Culver, “Mapping distributed brain function and networks with diffuse optical tomography,” Nature Photonics 8, 448–454 (2014).
[Crossref] [PubMed]

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
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S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

Springett, R.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Srinivasan, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30(15), 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
[Crossref]

Styles, I. B.

H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
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H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
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J. Duan, Z. Pan, B. Zhang, W. Liu, and X. Tai, “Fast algorithm for color texture image inpainting using the non-local CTV model,” Journal of Global Optimization 62(4), 853–876 (2015).
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J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomedical Signal Processing and Control 24, 120–127 (2016).
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V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3(5), 943–957 (2012).
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H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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Tichauer, K. M.

H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
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Tizzard, A.

Tosteson, T. D.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography,” Proceedings of the National Academy of Sciences 100(21), 12349–12354 (2003).
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A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
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J-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Transactions on Medical Imaging 30(5), 1143–1153 (2011).
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H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Physics in Medicine and Biology 48(16), 2713 (2003).
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C. Vonesch and M. Unser, “A fast iterative thresholding algorithm for wavelet-regularized deconvolution,” Proc. SPIE 6701, 1–5 (2007).

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J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
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J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
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Wei, W.

J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
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A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010).
[Crossref]

Wells, W. A.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technology in Cancer Research and Treatment 4(5), 513–526, 2005.
[Crossref] [PubMed]

White, B. R.

A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48(10), D137–D143 (2009).
[Crossref] [PubMed]

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
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S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Transactions on Signal Processing 57(7), 2479–2493 (2009).
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H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
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X. Wu, A. T. Eggebrecht, S. L. Ferradal, J. P. Culver, and H. Dehghani, “Quantitative evaluation of atlas-based high-density diffuse optical tomography for imaging of the human visual cortex,” Biomedical Optics Express 5(11), 3882–3900 (2014).
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Yalavarthy, P. K.

C. B. Shaw and P. K. Yalavarthy, “Performance evaluation of typical approximation algorithms for nonconvex lp-minimization in diffuse optical tomography,” J. Opt. Soc. Am. A 31(4), 852–862 (2014).
[Crossref]

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
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R. P. K. Jagannath and P. K. Yalavarthy, “Nonquadratic penalization improves near-infrared diffuse optical tomography,” J. Opt. Soc. Am. A 30(8), 1516–1523 (2013).
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J. Prakash and P. K. Yalavarthy, “A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography,” Medical Physics 40(3), 033101 (2013).
[Crossref] [PubMed]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using L1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17(8), 0860091 (2012).
[Crossref]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Communications in Numerical Methods in Engineering 25(6), 711–732 (2009).
[Crossref]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).
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J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Medical Physics 30(2), 235–247 (2003).
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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]

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,” Proceedings of the National Academy of Sciences 104(29), 12169–12174 (2007).
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Zhan, Y.

Y. Zhan, A. T. Eggebrecht, J. P. Culver, and H. Dehghani, “Singular value decomposition based regularization prior to spectral mixing improves crosstalk in dynamic imaging using spectral diffuse optical tomography,” Biomed. Opt. Express 3(9), 2036–2049 (2012).
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A. T. Eggebrecht, B. R. White, S. L. Ferradal, C. Chen, Y. Zhan, A. Z. Snyder, H. Dehghani, and J. P. Culver, “A quantitative spatial comparison of high-density diffuse optical tomography and fmri cortical mapping,” Neuroimage 61(4), 1120–1128 (2012).
[Crossref] [PubMed]

Zhang, B.

J. Duan, Z. Pan, B. Zhang, W. Liu, and X. Tai, “Fast algorithm for color texture image inpainting using the non-local CTV model,” Journal of Global Optimization 62(4), 853–876 (2015).
[Crossref]

Zhang, C.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical lp minimization algorithms,” Neurocomputing 119, 413–424 (2013).
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Zhang, Y.

E. T. Hale, W. Yin, and Y. Zhang, “A fixed-point continuation method for L1-regularized minimization with applications to compressed sensing,” CAAM TR07-07, Rice University (2007).

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H. Niu, S. Khadka, F. Tian, Z. Lin, C. Lu, C. Zhu, and H. Liu, “Resting-state functional connectivity assessed with two diffuse optical tomographic systems,” J. Biomed. Opt. 16(4), 046006 (2011).
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H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Applied Optics 42(1), 135–145 (2003).
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S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Applied Optics 44(10), 1858–1869 (2005).
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Biomed. Opt. Express (4)

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H-Y. Wu, A. Filer, I. B. Styles, and H. Dehghani, “Development of a multi-wavelength diffuse optical tomography system for early diagnosis of rheumatoid arthritis: simulation, phantoms and healthy human studies,” Biomedical Optics Express 7(11), 4769–4786 (2016).
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X. Wu, A. T. Eggebrecht, S. L. Ferradal, J. P. Culver, and H. Dehghani, “Quantitative evaluation of atlas-based high-density diffuse optical tomography for imaging of the human visual cortex,” Biomedical Optics Express 5(11), 3882–3900 (2014).
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H. R. A. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomedical Optics Express 3(9), 2131–2141 (2012).
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Communications in Numerical Methods in Engineering (1)

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J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan, and L. Bai, “An edge-weighted second order variational model for image decomposition,” Digital Signal Processing 49, 162–181 (2016).
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EURASIP Journal on Image and Video Processing (1)

J. Duan, Z. Pan, X. Yin, W. Wei, and G. Wang, “Some fast projection methods based on Chan-Vese model for image segmentation,” EURASIP Journal on Image and Video Processing 2014(1), 1–16 (2014).
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J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20(2), 74–82 (2014).
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IEEE Signal Processing Magazine (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Processing Magazine 18(6), 57–75 (2001).
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Mathematical Methods in the Applied Sciences (1)

W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu, and L. Bai, “Implementation of high-order variational models made easy for image processing,” Mathematical Methods in the Applied Sciences 39, 4208–4233 (2016).
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Figures (13)

Fig. 1
Fig. 1 Flow chart for SCDOT image reconstruction using the proposed spectral-L1 model.
Fig. 2
Fig. 2 L-curves (data fit against model regularization) derived from a synthetic example: a) Tikhonov regularization; b) L1 regularization using the IRLS algorithm; c) L1 regularization using the ADMM algorithm; d) L1 regularization using the FISTA algorithm. The optimal regularization parameter is around the point of maximum curvature (within the red boxes).
Fig. 3
Fig. 3 Three-dimensional surface mesh for each of the five head layers.
Fig. 4
Fig. 4 Schematic view from three directions showing the distribution of the imaging array with 158 sources (blue circles) and 166 detectors (red circles).
Fig. 5
Fig. 5 Ground-truth image with the activation only exists in the gray matter and white matter. (a): Illustration of the overall distribution of slices. (b)–(c): Individual activation is color-coded in red and represents the individual simulation of HbO2. (d)–(e): Individual activation is color-coded in green and represents the individual simulation of Hb.
Fig. 6
Fig. 6 The reconstructed image of the change of HbO2 and Hb in mM with noise-free data. Some examples of reconstruction artefacts are highlighted in green ellipses.
Fig. 7
Fig. 7 The reconstructed image of the change of HbO2 and Hb in mM with data contaminated by 1% Gaussian noise. Some examples of reconstruction artefacts are highlighted in green ellipses.
Fig. 8
Fig. 8 Evaluation metrics comparing the performance of different methods on a simulated 3D head model at five different noise levels. Left to right column: AC index; PC index and PSNR index. The first row gives the results from HbO2; the second row from Hb.
Fig. 9
Fig. 9 Ground-truth image showing the change in chromophore concentration confined to the gray matter.
Fig. 10
Fig. 10 Reconstruction of HbO2 and Hb using (L–R): Tikhonov for L2-norm regularization; IRLS, ADMM, FISTA algorithms for L1-norm regularization with different noise levels. First two rows: results with clean simulated data; Last two rows: those with noisy data.
Fig. 11
Fig. 11 (a): Illustration of the overall distribution of slices. (b): Distribution of sources and detectors.
Fig. 12
Fig. 12 Ground truth and reconstruction results with different regularizations. From left to right: ground truth; results with L2 regularization; results with L1 regularization using FISTA algorithm.
Fig. 13
Fig. 13 Total CPU time consumed in the experiments described in section 5.2

Tables (9)

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Algorithm 1: Gauss-Newton Algorithm for Minimizing Eq. (3).

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Algorithm 2: Iteratively Reweighted Least Square Algorithm (IRLS)

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Algorithm 3: Alternating Directional Method of Multipliers (ADMM)

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Algorithm 4: Fast Iterative Shrinkage-Thresholding Algorithm (FISTA)

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Table 1 Head tissue optical property for each of five layers.

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Table 2 Three evaluation metrics for HbO2 on results by different methods

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Table 3 Three evaluation metrics for Hb on results by different methods

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Table 4 Evaluation of L1 and L2 regularization methods for reconstruction of a single rod inclusion in a tissue-simulating phantom.

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Table 5 Total CPU time(s) consumed in the inverse model for the experiments described in section 5.2

Equations (28)

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κ ( r , λ i ) Φ ( r , λ i ) + μ a ( r , λ i ) Φ ( r , λ i ) = q 0 ( r , λ i ) .
( μ a , λ 1 μ a , λ 2 ) = ( ε c 1 , λ 1 ε c 2 , λ 1 ε c 1 , λ 2 ε c 2 , λ 2 ) ( c 1 c 2 ) ,
c 1 , c 2 = arg min c 1 , c 2 ( Φ λ 1 M Φ λ 2 M ) ( Φ λ 1 C ( k ) Φ λ 2 C ( k ) ) 2 2 ,
( Φ λ 1 C ( k ) Φ λ 2 C ( k ) ) = ( Φ λ 1 C ( k 1 ) Φ λ 2 C ( k 1 ) ) + J k 1 ( c 1 k c 1 k 1 c 2 k c 2 k 1 ) ,
J = ( Φ λ 1 C c 1 Φ λ 1 C c 2 Φ λ 2 C c 1 Φ λ 2 C c 2 ) = ( Φ λ 1 C μ a , λ 1 μ a , λ 1 c 1 Φ λ 1 C μ a , λ 1 μ a , λ 1 c 2 Φ λ 2 C μ a , λ 2 μ a , λ 2 c 1 Φ λ 2 C μ a , λ 2 μ a , λ 2 c 2 ) = ( J λ 1 ε c 1 , λ 1 J λ 1 ε c 2 , λ 1 J λ 2 ε c 1 , λ 2 J λ 2 ε c 2 , λ 2 ) ,
Δ c k = arg min Δ c Δ Φ k 1 J k 1 Δ c 2 2 ,
Δ c k = ( Δ c 1 k Δ c 2 k ) = ( c 1 k c 1 k 1 c 2 k c 2 k 1 ) .
Δ Φ k 1 = ( Φ λ 1 M Φ λ 1 C ( k 1 ) Φ λ 2 M Φ λ 2 C ( k 1 ) ) .
( J ( k 1 ) T J ( k 1 ) ) Δ c k = J ( k 1 ) T Δ Φ k 1 .
Δ c k = arg min Δ c { Δ Φ k 1 J k 1 Δ c 2 2 + λ Δ c 2 2 } .
Δ c k = ( J ( k 1 ) T J ( k 1 ) + λ I ) 1 J ( k 1 ) T Δ Φ k 1 .
Δ c k = arg min Δ c { Δ Φ k 1 J k 1 Δ c 2 2 + λ Δ c 1 } .
Δ c k = arg min Δ c { Δ Φ k 1 J k 1 Δ c 2 2 + λ W Δ c 2 2 } .
w s = { | Δ c s i 1 | 0.5 if | Δ c s i 1 | ε ε 1 if | Δ c s i 1 | < ε .
( J ( k 1 ) T J ( k 1 ) + λ W T W ) Δ c = J ( k 1 ) T Δ Φ k 1 .
Δ c , v , b = arg min Δ c , v , b { Δ Φ k 1 J k 1 Δ c 2 2 + λ v 1 + θ 2 v Δ c b 2 2 } .
( J ( k 1 ) T J ( k 1 ) + θ I ) Δ c = J ( k 1 ) T Δ Φ k 1 + θ ( v i 1 b i 1 ) .
λ v | v | + θ ( v Δ c i b i 1 ) = 0 ,
v i = max ( | Δ c i + b i 1 | λ θ , 0 ) sign ( Δ c i + b i 1 ) ,
Δ c i = Δ c i 1 t F ( Δ c i 1 ) ,
Δ c = arg min Δ c { F ( Δ c i 1 ) + F ( Δ c i 1 ) ( Δ c Δ c i 1 ) + 1 2 t Δ c Δ c i 1 2 2 } .
Δ c = arg min Δ c { 1 2 t Δ c i 1 t F ( Δ c i 1 ) Δ c 2 2 + λ Δ c 1 } .
Δ c i = max ( | Δ c i 1 t F ( Δ c i 1 ) | t λ , 0 ) sign ( Δ c i 1 t F ( Δ c i 1 ) ) .
Δ c i = max ( | Δ y i t F ( Δ y i ) | t λ , 0 ) sign ( Δ y i t F ( Δ y i ) ) ,
AC = j = 1 N c i j / N c ˜ i i = 1 , 2
PC = COV ( c i , c ˜ i ) σ ( c i ) σ ( c ˜ i ) i = 1 , 2 .
PSNR = 10 log 10 ( MAX c i 2 MSE ) i = 1 , 2 .
MSE = 1 N j = 1 N ( c i j c ˜ i j ) 2

Metrics