Abstract

We present an image reconstruction method for diffuse optical tomography (DOT) by using the sparsity regularization and expectation-maximization (EM) algorithm. Typical image reconstruction approaches in DOT employ Tikhonov-type regularization, which imposes restrictions on the L 2 norm of the optical properties (absorption/scattering coefficients). It tends to cause a blurring effect in the reconstructed image and works best when the unknown parameters follow a Gaussian distribution. In reality, the abnormality is often localized in space. Therefore, the vector corresponding to the change of the optical properties compared with the background would be sparse with only a few elements being nonzero. To incorporate this information and improve the performance, we propose an image reconstruction method by regularizing the L 1 norm of the unknown parameters and solve it iteratively using the expectation-maximization algorithm. We verify our method using simulated 3D examples and compare the reconstruction performance of our approach with the level-set algorithm, Tikhonov regularization, and simultaneous iterative reconstruction technique (SIRT). Numerical results show that our method provides better resolution than the Tikhonov-type regularization and is also efficient in estimating two closely spaced abnormalities.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]

2007

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

2006

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

2005

D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process. 53, 3010-3022 (2005).
[CrossRef]

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. Boas, "Optimal linear inverse solution with multiple priors in diffuse optical tomography," Appl. Opt. 44, 1948-1956 (2005).
[CrossRef] [PubMed]

2004

J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory 50, 1341-1344 (2004).
[CrossRef]

2003

2002

G. Strangman, D. Boas, and J. Sutton, "Non-invasive neuroimaging using near-infrared light," Biol. Psychiatry 52, 679-693 (2002).
[CrossRef] [PubMed]

2001

M. Cetin and W. C. Karl, "Feature-enhanced synthetic aperture radar image formation bsed on nonquadratic regularization," IEEE Trans. Image Process. 10, 623-631 (2001).
[CrossRef]

2000

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, D. Boas, and D. Brook, "A shape-based reconstruction technique for DPDW data," Opt. Express 72, 481-491 (2000).
[CrossRef]

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

1999

B. Pogue, T. McBride, J. Prewitt, U. Osterberg, and K. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Opt. 38, 2950-2961 (1999).
[CrossRef]

P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes uisng generalized-Gaussion and complexity priors," IEEE Trans. Inf. Theory 45, 909-919 (1999).
[CrossRef]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. Eng. 15, R41-R93 (1999).
[CrossRef]

1998

P. S. Bradley, O. L. Mangasarian, and W. N. Street, "Feature selection via mathematical programming," INFORMS J. Comput. 10, 209-217 (1998).
[CrossRef]

1997

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

K. Matsuura and Y. Okabe, "A robust reconstruction of sparse biomagnetic sources," IEEE Trans. Biomed. Eng. 44, 720-726 (1997).
[CrossRef] [PubMed]

I. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process. 45, 600-616 (1997).
[CrossRef]

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

1996

1995

R. Aronson, "Boundary conditions for diffusion of light," J. Opt. Soc. Am. A 12, 2532-2539 (1995).
[CrossRef]

D. L. Donoho, "De-noising by soft-threshold," IEEE Trans. Inf. Theory 41, 613-627 (1995).
[CrossRef]

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 619-701 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

K. Matsuura and Y. Okabe, "Selective minimum-norm solution of the biomagnetic inverse problem," IEEE Trans. Biomed. Eng. 42, 608-615 (1995).
[CrossRef] [PubMed]

1994

D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

1989

1983

C. Wu, "One the convergence properties of the EM algorithm," Ann. Stast. 11, 95-103 (1983).
[CrossRef]

Aronson, R.

Arridge, S. R.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. Eng. 15, R41-R93 (1999).
[CrossRef]

Aubert, G.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

Barbaro, A.

Barlaud, M.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

Blanc-Feraud, L.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

Boas, D.

Boas, D. A.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Boverman, G.

Bradley, P. S.

P. S. Bradley, O. L. Mangasarian, and W. N. Street, "Feature selection via mathematical programming," INFORMS J. Comput. 10, 209-217 (1998).
[CrossRef]

Brook, D.

M. E. Kilmer, E. L. Miller, D. Boas, and D. Brook, "A shape-based reconstruction technique for DPDW data," Opt. Express 72, 481-491 (2000).
[CrossRef]

Brooks, D.

Brooks, D. H.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Brooksby, B. A.

Butler, J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Cetin, M.

D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process. 53, 3010-3022 (2005).
[CrossRef]

M. Cetin and W. C. Karl, "Feature-enhanced synthetic aperture radar image formation bsed on nonquadratic regularization," IEEE Trans. Image Process. 10, 623-631 (2001).
[CrossRef]

Chance, B.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

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

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef]

Charbonnier, P.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

Chen, Y.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

Dale, A.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Dehghani, H.

DiMarzio, C. A.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Donoho, D.

D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

Donoho, D. L.

D. L. Donoho, "De-noising by soft-threshold," IEEE Trans. Inf. Theory 41, 613-627 (1995).
[CrossRef]

Douiri, A.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

Feng, T.-C.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, "Adaptive sparseness for supervised learning," IEEE Trans. Pattern Anal. Mach. Intell. 25, 1150-1159 (2003).
[CrossRef]

M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Transactions on Image Processing 12, 906-916 (2003).
[CrossRef]

Fishkin, J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Fuchs, J.-J.

J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory 50, 1341-1344 (2004).
[CrossRef]

Ganive, J.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Gaudette, R. J.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Gaudette, T.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Gorodnitsky, I.

I. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process. 45, 600-616 (1997).
[CrossRef]

Grosenick, D.

Halgren, E.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Harrington, D.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Haskell, R. C.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

Hillman, E. M. C.

Holboke, M. J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Huang, M.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Intes, X.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

Jiang, H.

K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through totalvariation minimization," Appl. Opt. 35, 3447-3458 (1996).
[CrossRef] [PubMed]

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 619-701 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

Jiang, S.

Johnstone, I.

D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

Karl, W. C.

M. Cetin and W. C. Karl, "Feature-enhanced synthetic aperture radar image formation bsed on nonquadratic regularization," IEEE Trans. Image Process. 10, 623-631 (2001).
[CrossRef]

Kidney, D.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Kilmer, M. E.

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. Boas, "Optimal linear inverse solution with multiple priors in diffuse optical tomography," Appl. Opt. 44, 1948-1956 (2005).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, A. Barbaro, and D. Boas, "Three-dimensional shaped-based imaging of absorption perturbation for diffuse optical tomography," Appl. Opt. 42, 3129-3144 (2003).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, D. Boas, and D. Brook, "A shape-based reconstruction technique for DPDW data," Opt. Express 72, 481-491 (2000).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Lee, R.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Lewis, S.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Li, A.

Li, X.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Liu, J.

P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes uisng generalized-Gaussion and complexity priors," IEEE Trans. Inf. Theory 45, 909-919 (1999).
[CrossRef]

Macdonald, R.

Malioutov, D.

D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process. 53, 3010-3022 (2005).
[CrossRef]

Mangasarian, O. L.

P. S. Bradley, O. L. Mangasarian, and W. N. Street, "Feature selection via mathematical programming," INFORMS J. Comput. 10, 209-217 (1998).
[CrossRef]

Matsuura, K.

K. Matsuura and Y. Okabe, "A robust reconstruction of sparse biomagnetic sources," IEEE Trans. Biomed. Eng. 44, 720-726 (1997).
[CrossRef] [PubMed]

K. Matsuura and Y. Okabe, "Selective minimum-norm solution of the biomagnetic inverse problem," IEEE Trans. Biomed. Eng. 42, 608-615 (1995).
[CrossRef] [PubMed]

McAdams, M. S.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

McBride, T.

Miller, E. L.

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. Boas, "Optimal linear inverse solution with multiple priors in diffuse optical tomography," Appl. Opt. 44, 1948-1956 (2005).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, A. Barbaro, and D. Boas, "Three-dimensional shaped-based imaging of absorption perturbation for diffuse optical tomography," Appl. Opt. 42, 3129-3144 (2003).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, D. Boas, and D. Brook, "A shape-based reconstruction technique for DPDW data," Opt. Express 72, 481-491 (2000).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

Moesta, T.

Moulin, P.

P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes uisng generalized-Gaussion and complexity priors," IEEE Trans. Inf. Theory 45, 909-919 (1999).
[CrossRef]

Mucke, J.

Nioka, S.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

Nowak, R. D.

M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Transactions on Image Processing 12, 906-916 (2003).
[CrossRef]

Okabe, Y.

K. Matsuura and Y. Okabe, "A robust reconstruction of sparse biomagnetic sources," IEEE Trans. Biomed. Eng. 44, 720-726 (1997).
[CrossRef] [PubMed]

K. Matsuura and Y. Okabe, "Selective minimum-norm solution of the biomagnetic inverse problem," IEEE Trans. Biomed. Eng. 42, 608-615 (1995).
[CrossRef] [PubMed]

Osterberg, U.

Patterson, M. S.

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef]

Paulsen, K.

Paulsen, K. D.

H. Dehghani, B.W. Pogue, S. Jiang, B. A. Brooksby, and K. D. Paulsen, "Three-dimensional optical tomography: Resolution in small-object imaging," Appl. Opt. 42, 3117-3128 (2003).
[CrossRef] [PubMed]

K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through totalvariation minimization," Appl. Opt. 35, 3447-3458 (1996).
[CrossRef] [PubMed]

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 619-701 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

Podgorny, I.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Pogue, B.

Pogue, B. W.

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

Pogue, B.W.

Prewitt, J.

Rao, B. D.

I. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process. 45, 600-616 (1997).
[CrossRef]

Riley, J.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

Rinnerberg, H.

Ripoll, J.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

Schlag, P.

Schweiger, M.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

Shah, N.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Song, T.

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Strangman, G.

G. Strangman, D. Boas, and J. Sutton, "Non-invasive neuroimaging using near-infrared light," Biol. Psychiatry 52, 679-693 (2002).
[CrossRef] [PubMed]

Street, W. N.

P. S. Bradley, O. L. Mangasarian, and W. N. Street, "Feature selection via mathematical programming," INFORMS J. Comput. 10, 209-217 (1998).
[CrossRef]

Stroszcynski, C.

Sutton, J.

G. Strangman, D. Boas, and J. Sutton, "Non-invasive neuroimaging using near-infrared light," Biol. Psychiatry 52, 679-693 (2002).
[CrossRef] [PubMed]

Svaasand, L. O.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

Tibshirani, R.

R. Tibshirani, "Regression shrinkage and selection via the Lasso," J. R. Stat. Soc. Ser. B 58, 267-288 (1996).

Tromberg, B. J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Tsay, T.-T.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

Villringer, A.

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

Wabnitz, H.

Willsky, A. S.

D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process. 53, 3010-3022 (2005).
[CrossRef]

Wilson, B. C.

Wu, C.

C. Wu, "One the convergence properties of the EM algorithm," Ann. Stast. 11, 95-103 (1983).
[CrossRef]

Yodh, A.

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

Zhang, Q.

Zhang, Y.

Ann. Stast.

C. Wu, "One the convergence properties of the EM algorithm," Ann. Stast. 11, 95-103 (1983).
[CrossRef]

Appl. Opt.

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef]

B. Pogue, T. McBride, J. Prewitt, U. Osterberg, and K. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Opt. 38, 2950-2961 (1999).
[CrossRef]

K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through totalvariation minimization," Appl. Opt. 35, 3447-3458 (1996).
[CrossRef] [PubMed]

H. Dehghani, B.W. Pogue, S. Jiang, B. A. Brooksby, and K. D. Paulsen, "Three-dimensional optical tomography: Resolution in small-object imaging," Appl. Opt. 42, 3117-3128 (2003).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, A. Barbaro, and D. Boas, "Three-dimensional shaped-based imaging of absorption perturbation for diffuse optical tomography," Appl. Opt. 42, 3129-3144 (2003).
[CrossRef] [PubMed]

D. Grosenick, T. Moesta, H. Wabnitz, J. Mucke, C. Stroszcynski, R. Macdonald, P. Schlag, and H. Rinnerberg, "Time-domain optical mammography: Initial clinial results on detection and characterization of breast tumors," Appl. Opt. 42, 3170-3186 (2003).
[CrossRef] [PubMed]

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. Boas, "Optimal linear inverse solution with multiple priors in diffuse optical tomography," Appl. Opt. 44, 1948-1956 (2005).
[CrossRef] [PubMed]

Biol. Psychiatry

G. Strangman, D. Boas, and J. Sutton, "Non-invasive neuroimaging using near-infrared light," Biol. Psychiatry 52, 679-693 (2002).
[CrossRef] [PubMed]

Biometrika

D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

IEEE Trans. Biomed. Eng.

K. Matsuura and Y. Okabe, "Selective minimum-norm solution of the biomagnetic inverse problem," IEEE Trans. Biomed. Eng. 42, 608-615 (1995).
[CrossRef] [PubMed]

K. Matsuura and Y. Okabe, "A robust reconstruction of sparse biomagnetic sources," IEEE Trans. Biomed. Eng. 44, 720-726 (1997).
[CrossRef] [PubMed]

IEEE Trans. Image Process.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-perserving regularization in computed imaging," IEEE Trans. Image Process. 6, 298-310 (1997).
[CrossRef] [PubMed]

M. Cetin and W. C. Karl, "Feature-enhanced synthetic aperture radar image formation bsed on nonquadratic regularization," IEEE Trans. Image Process. 10, 623-631 (2001).
[CrossRef]

IEEE Trans. Inf. Theory

D. L. Donoho, "De-noising by soft-threshold," IEEE Trans. Inf. Theory 41, 613-627 (1995).
[CrossRef]

P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes uisng generalized-Gaussion and complexity priors," IEEE Trans. Inf. Theory 45, 909-919 (1999).
[CrossRef]

J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory 50, 1341-1344 (2004).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

M. A. T. Figueiredo, "Adaptive sparseness for supervised learning," IEEE Trans. Pattern Anal. Mach. Intell. 25, 1150-1159 (2003).
[CrossRef]

IEEE Trans. Signal Process.

D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process. 53, 3010-3022 (2005).
[CrossRef]

I. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process. 45, 600-616 (1997).
[CrossRef]

IEEE Transactions on Image Processing

M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Transactions on Image Processing 12, 906-916 (2003).
[CrossRef]

INFORMS J. Comput.

P. S. Bradley, O. L. Mangasarian, and W. N. Street, "Feature selection via mathematical programming," INFORMS J. Comput. 10, 209-217 (1998).
[CrossRef]

Inverse Probl. Eng.

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. Eng. 15, R41-R93 (1999).
[CrossRef]

J. Biomed. Opt.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, "Threedimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-247 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, and M. S. McAdams, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. 10, 2727-2741 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. R. Stat. Soc. Ser. B

R. Tibshirani, "Regression shrinkage and selection via the Lasso," J. R. Stat. Soc. Ser. B 58, 267-288 (1996).

Meas. Sci. Technol.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, "Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information," Meas. Sci. Technol. 18, 87-95 (2007).
[CrossRef]

Med. Phys.

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 619-701 (1995).
[CrossRef]

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. Yodh, and B. Chance, "In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green," Med. Phys. 30, 1039-1047 (2003).
[CrossRef] [PubMed]

NeuroImage

M. Huang, A. Dale, T. Song, E. Halgren, D. Harrington, I. Podgorny, J. Ganive, S. Lewis, and R. Lee, "Vectorbased spatial-temporal minimum L1-norm solution for MEG," NeuroImage 31, 1025-1037 (2006).
[CrossRef] [PubMed]

Opt. Express

M. E. Kilmer, E. L. Miller, D. Boas, and D. Brook, "A shape-based reconstruction technique for DPDW data," Opt. Express 72, 481-491 (2000).
[CrossRef]

Phys. Med. Biol.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol. 45, 1051-1070 (2000).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, "Initial assessment of a simple system for frequency domain diffuse optical tomography," Phys. Med. Biol. 40, 1709-1729 (1995).
[CrossRef] [PubMed]

Trends Neurosci.

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

Other

A. N. Tikhonov and V. Y. Arsenin, Solutions of ill-posed problems (V. H. Winston Sons, Washington D. C.).

S.-J. Kim, K. Koh,M. Lustig, S. Boyd, and D. Gorinevsky, "An efficient method for l1-regularized least squares," IEEE Trans. Sel. Top. Signal Process. (2007).

G. McLachlan and T. Krishnan, EM algorithm and extensions (Wiley, New York).

M. A. O’Leary, "Imaging with diffuse photon density waves," Ph.D. thesis, University of Pennsylvania (1996).

M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, "Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging," J. Biomed. Opt. 11, 064,029-1-12 (2006).
[CrossRef]

O. Dorn, "A shape reconstruction method for diffuse optical tomography using a transport model and level sets," in Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 1015-1018 (2006).

G. Boverman and E. Miller, "Estimation-theoretic algorithms and bounds for three-dimensional polar shapebased imaging in diffuse optical tomography," in Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 1132-1135 (2006).

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Figures (6)

Fig. 1.
Fig. 1.

Simulation setup. The domain is composed of an 8 × 8 × 6 cm3 cube, where twenty-five sources (circles) are placed on the bottom surface (z = 0 cm) and twenty-five detectors (black dots) on the top (z = 6 cm). The range along the x and y axes is [-4,4] cm.

Fig. 2.
Fig. 2.

Original δμ a distribution in cm-1, assuming only one absorbing abnormality. Small images show the cross-section layers at different z values at 0.5 cm intervals.

Fig. 3.
Fig. 3.

Reconstructed δμ a distributions in cm-1, assuming only one absorbing abnormality as shown in Fig. 2. (a) Using the sparse regularization with EM algorithm; (b) using the level-set algorithm; (c) using the Tikhonov regularization; (d) using SIRT. Small images show the cross-section layers at different z values at 0.5 cm intervals.

Fig. 4.
Fig. 4.

Original δμ a distributions in cm-1, assuming two spherical absorptive abnormalities.

Fig. 5.
Fig. 5.

Reconstructed δμ a distributions in cm-1, assuming two spherical absorptive abnormalities as shown in Fig. 4(a). (a) Using the sparse regularization with EM algorithm; (b) using the level-set algorithm; (c) using the Tikhonov regularization; (d) using SIRT.

Fig. 6.
Fig. 6.

Reconstructed δμ a distributions in cm-1, assuming two spherical absorptive abnormalities as shown in Fig. 4(b). (a) Using the sparse regularization with EM algorithm; (b) using the level-set algorithm; (c) using the Tikhonov regularization; (d) using SIRT.

Equations (36)

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

ϕ c = A c μ ,
ϕ = ,
y = + e ,
e ~ N ( 0 , σ 2 I ) ,
μ ̂ = arg   max μ { y 2 γ g ( μ ) } ,
g ( μ ) = μ 2 2 = i μ i 2 ,
μ ̂ = ( A T A + γI ) # A T y ,
μ ̂ = arg   max μ { ln p ( y μ ) + γ ln p ( μ ) } ,
x 1 = i x i .
min μ 1 subject to y ξ 2 ,
μ ̂ = arg   max μ { y 2 2 γ μ 1 } .
μ ̂ = arg   max μ { log p ( y μ ) γ μ 1 }
= arg   max μ { y 2 2 2 σ 2 γ μ 1 } ,
{ x = μ + αe 1 , y = Ax + e 2 ,
e = α Ae 1 + e 2 ,
e 1 ~ N ( 0 , I ) ,
e 2 ~ N ( 0 , σ 2 I α 2 AA T ) .
α 2 α 2 β 1 ,
Q ( μ , μ ̂ ( k ) ) = E [ log p ( y , x μ ) y , μ ̂ ( k ) ] .
x ̂ ( k ) = μ ̂ ( k ) + α 2 σ 2 A T ( y A μ ̂ ( k ) ) .
μ ̂ ( k + 1 ) = arg   max μ { Q ( μ , μ ̂ ( k ) ) g ( μ ) } ,
μ ̂ ( k + 1 ) = arg   max μ { μ x ̂ ( k ) 2 2 α 2 γ μ 1 }
= arg   max μ { μ x ̂ ( k ) 2 2 α 2 γ μ 1 } .
μ ^ i ( k + 1 ) = arg   max μ i { μ i 2 + 2 μ i x i 2 α 2 γ μ i } ,
μ ^ i ( k + 1 ) = sgn ( x ^ i ( k ) ) ( x ̂ i ( k ) γα 2 ) + ,
log p ( y μ ̂ ( k + 1 ) ) γ μ ( k + 1 ) 1 log p ( y μ ̂ ( k ) ) γ μ ( k ) 1 .
α 2 γ ( α 2 γ ) max = x ,
σ 2 γ ( σ 2 γ ) max = A T y .
p ( y , x μ ) = p ( y x , μ ) p ( x μ ) = p ( y x ) p ( x μ ) ,
log p ( y , x μ ) = x μ 2 2 α 2 + C 1
= μ T μ 2 μ T x 2 α 2 + C 2 ,
x ̂ ( k ) = E [ x y , μ ̂ ( k ) ] = xp ( x y , μ ̂ ( k ) ) dx .
y x ~ N ( Ax , σ 2 I α 2 AA T ) ,
x μ ̂ ( k ) ~ N ( μ ̂ ( k ) , α 2 I ) ,
p ( x y , μ ̂ ( k ) ) = p ( y x ) p ( x μ ( k ) ) p ( y μ ( k ) ) ∝p ( y x ) p ( x μ ( k ) ) ,
x ̂ ( k ) = μ ̂ ( k ) + α 2 σ 2 A T ( y A μ ̂ ( k ) ) .

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