Abstract

Near-Infrared (NIR) tomographic image reconstruction is a non-linear, ill-posed and ill-conditioned problem, and so in this study, different ways of penalizing the objective function with structural information were investigated. A simple framework to incorporate structural priors is presented, using simple weight matrices that have either Laplacian or Helmholtz-type structures. Using both MRI-derived breast geometry and phantom data, a systematic and quantitative comparison was performed with and without spatial priors. The Helmholtz-type structure can be seen as a more generalized approach for incorporating spatial priors into the reconstruction scheme. Moreover, parameter reduction (i.e. hard prior information) in the imaging field through the enforcement of spatially explicit regions may lead to erroneous results with imperfect spatial priors.

© 2007 Optical Society of America

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Direct regularization from co-registered anatomical images for MRI-guided near-infrared spectral tomographic image reconstruction

Limin Zhang, Yan Zhao, Shudong Jiang, Brian W. Pogue, and Keith D. Paulsen
Biomed. Opt. Express 6(9) 3618-3630 (2015)

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2007 (1)

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

2006 (2)

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[Crossref] [PubMed]

2005 (6)

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

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

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (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, 1968–1970 (2005).
[Crossref] [PubMed]

2004 (2)

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

2003 (7)

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

Q. Zhu, N. G. Chen, and S. C. Kurtzman, “Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound,” Opt. Lett. 28, 337–339 (2003).
[Crossref] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[Crossref]

H. Dehghani, B.W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42, 3117–3126 (2003).
[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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
[Crossref]

2002 (1)

M. F. Ernst and J. A. Roukema, “Diagnosis of non-palpable breast cancer: a review,” The Breast 11, 13 (2002).
[Crossref]

2001 (3)

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

2000 (2)

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[Crossref] [PubMed]

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
[Crossref]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inv. Problems 15, R41–R93 (1999).
[Crossref]

1998 (1)

V. Ntziachristos, X. H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[Crossref]

1997 (1)

1996 (1)

1995 (4)

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

H. Jiang, K. D. Paulsen, U. Osterberg, B.W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[Crossref] [PubMed]

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
[Crossref]

1963 (2)

D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

A. N. Tikhonov, “Regularization of mathematically incorrectly posed problems,” Soviet Math. Dokl. 4, 1624–1627 (1963).

1944 (1)

K. Levenberg, “A method for the solution of certain nonlinear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Abele, C.

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[Crossref] [PubMed]

Aronson, R.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
[Crossref]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inv. Problems 15, R41–R93 (1999).
[Crossref]

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

Barbour, R. L.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
[Crossref]

Barbour, S. L. S.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
[Crossref]

Bartel, S.

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[Crossref] [PubMed]

Boas, D.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Boas, D. A.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

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

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Boverman, G.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

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

Brooks, D.

Brooks, D. H.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Brooksby, B.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[Crossref]

H. Dehghani, B.W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42, 3117–3126 (2003).
[Crossref] [PubMed]

B. Brooksby, Combining near infrared tomography and magnetic resonance imaging to improve breast tissue chromophore and scattering assessment, Ph.D. Thesis, Dartmouth College, May 2005.
[PubMed]

Brukilacchio, T. J.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[Crossref] [PubMed]

Chance, B.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
[Crossref]

V. Ntziachristos, X. H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[Crossref]

Chang, J. W.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
[Crossref]

Chaves, T.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[Crossref] [PubMed]

Chen, N. G.

Chorlton, M.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[Crossref] [PubMed]

Dehghani, H.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[Crossref]

H. Dehghani, B.W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42, 3117–3126 (2003).
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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,” Appl. Opt. 42, 135–145 (2003).
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S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
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DiMarzio, C. A.

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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Doyley, M.

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

Doyley, M. M.

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
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M. F. Ernst and J. A. Roukema, “Diagnosis of non-palpable breast cancer: a review,” The Breast 11, 13 (2002).
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Gaudette, R. J.

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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Gibson, J. J.

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

Graber, H. L.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
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A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
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Hillman, E.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

Hillman, E. M. C.

Hiroaka, M.

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
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Jiang, H.

Jiang, S.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
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X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (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, 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
[Crossref]

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Kaufman, H.

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
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Kilmer, M.

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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Kilmer, M. E.

Kogel, C.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

Koo, P. C.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
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Kopans, D. B.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
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Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

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

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
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D. R. Lynch, Numerical partial differential equations for environmental scientists and engineers - A first practical course, (Springer, Edition 1, 2005).
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Ma, X. H.

V. Ntziachristos, X. H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[Crossref]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
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McBride, T.

McBride, T. O.

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
[Crossref]

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

Miller, E. L.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

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

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Moore, R. H.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[Crossref] [PubMed]

Ntziachristos, V.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
[Crossref]

V. Ntziachristos, X. H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[Crossref]

Osterberg, U.

Osterberg, U. L.

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

Patterson, M. S.

Paulsen, K. D

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

Paulsen, K. D.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

H. Dehghani, B.W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42, 3117–3126 (2003).
[Crossref] [PubMed]

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[Crossref] [PubMed]

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. D. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Express 1, 391–403 (1997).
[Crossref] [PubMed]

H. Jiang, K. D. Paulsen, U. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[Crossref]

H. Jiang, K. D. Paulsen, U. Osterberg, B.W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Paulsen, K.D.

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

Pogue, B. W

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

Pogue, B. W.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequencydomain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[Crossref]

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[Crossref] [PubMed]

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. D. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Express 1, 391–403 (1997).
[Crossref] [PubMed]

H. Jiang, K. D. Paulsen, U. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[Crossref]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Pogue, B.W.

Poplack, S. P.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (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, 1968–1970 (2005).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

Poplack, S.P.

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

Rafferty, E.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

Roukema, J. A.

M. F. Ernst and J. A. Roukema, “Diagnosis of non-palpable breast cancer: a review,” The Breast 11, 13 (2002).
[Crossref]

Schnall, M.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
[Crossref]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]

Shudong, J.

Soho, S.

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

Song, X.

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Srinivasan, S.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[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, 1968–1970 (2005).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “ Effect of image reconstruction bias upon spectroscopy-based quantification of chromophores in near infrared tomography,” Proc. OSA Biomedical Topical Meetings, OSA Technical Digest, WB3:1-3, Optical Society of America, Washington, DC (2004).

Stott, J.

Stott, J. J.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

Testorf, M.

Tikhonov, A. N.

A. N. Tikhonov, “Regularization of mathematically incorrectly posed problems,” Soviet Math. Dokl. 4, 1624–1627 (1963).

Tosteson, T. D.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

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 andWater Concentration, Oxygen Saturation and Scattering Measured in Vivo by Near-Infrared Breast Tomography,” Proc. Nat. Acad. Sci. U.S.A. 100, 12349–12354 (2003).
[Crossref]

Wang, X.

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

Weaver, J.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using Hybrid MRI-Guided Near-Infrared Spectral Tomography,” Proc. Nat. Acad. Sci. U.S.A. 103, 8828–8833 (2006).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (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, 1968–1970 (2005).
[Crossref] [PubMed]

Weaver, J. B.

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast,” Rev. Sci. Instrum. 75, 5262–5270 (2004).
[Crossref]

Wells, W.A.

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

Wu, T.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
[Crossref] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[Crossref] [PubMed]

Yalavarthy, P. K.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[Crossref] [PubMed]

Yodh, A. G.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
[Crossref]

Zhang, Q.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
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A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. A. Boas, “Optimal linear inverse solution with multiple priors in diffuse optical tomography,” Appl. Opt. 44, 1948–1956 (2005).
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A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, and D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[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 Sig. Proc. Mag. 18, 57–75 (2001).
[Crossref]

Zhang, Y.

Zhu, Q.

Appl. Opt. (4)

IEEE Comp. Sci. Eng. (1)

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, “MRI-guided optical tomography: Prospects and computation for a new imaging method,” IEEE Comp. Sci. Eng. 2, 63–77 (1995).
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IEEE J. Sel. Top. Quantum Electron. (1)

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[Crossref]

IEEE Sig. Proc. Mag. (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 Sig. Proc. Mag. 18, 57–75 (2001).
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Inv. Problems (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inv. Problems 15, R41–R93 (1999).
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J Biomed. Opt. (1)

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J Biomed. Opt. 10, 024033:1-9 (2005).
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J. Biomed. Opt. (5)

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
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S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, “Improved quantification of small objects in near-infrared diffuse optical tomography,” J. Biomed. Opt. 9, 1161–1171 (2004).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. Biomed. Opt. 10, 051504:1-10 (2005).
[Crossref] [PubMed]

X. Wang, B.W. Pogue, S. Jiang, X. Song, K.D. Paulsen, C. Kogel, S.P. Poplack, and W.A. Wells, , “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 051704:1-8 (2005).
[Crossref] [PubMed]

B. W. Pogue, K. D. Paulsen, H. Kaufman, and C. Abele, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[Crossref] [PubMed]

J. Electron. Imaging (1)

S. Jiang, B. W. Pogue, T. O. McBride, M. M. Doyley, S. P. Poplack, and K. D. Paulsen, “Near-infrared breast tomography calibration with optoelastic tissue simulating phantoms,” J. Electron. Imaging 12, 613–620 (2003).
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J. Opt. Soc. Am. A (1)

J. Soc. Ind. Appl. Math. (1)

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Med. Phys. (3)

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The Finite Element Model for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys. 22, 1779–1792 (1995).
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K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
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Opt. Express (2)

Opt. Lett. (3)

Phys. Med. Biol. (1)

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Proc. Nat. Acad. Sci. U.S.A. (3)

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Nat. Acad. Sci. U.S.A. 97, 2767–2772 (2000).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Simulated μa and μ´ s distributions from a breast (obtained from a volunteer) are shown in the first column. Optical properties for the region labeled ‘0’ (fat) are: μa = 0.006 mm-1 and μs = 0.6 mm-1. Region ‘1’ (fibroglandular) values are: μa = 0.012 mm-1 and μ´ s = 1.2 mm-1. Region ‘2’ (tumor) values are: μa = 0.018 mm-1 and μ´ s = 1.8 mm-1. Reconstructed μa and μ´ s images from different techniques with simulated data having 1% random noise and imperfect structural information in defining region ‘1’ (7% reduction compared to the original segmentation) are shown in the rest of the columns. The middle two columns use soft prior structural information while the last column shows the result with hard prior information. In the Helmholtz case, κ = 1/8 mm-1 (BPE) was used. (b) Cross-sectional plots, along the dotted line in the actual image (see first column of (a)), of true and reconstructed μa and μ´ s distributions.

Fig. 2.
Fig. 2.

(a) Reconstructed μa and μ´ s images from different techniques with simulated data having 5% random noise and perfect structural priors (actual images are shown in the first column of Fig. 1(a)). The first column shows the reconstruction results without the use of prior information. The middle two columns use soft prior structural information while the last row shows the result with hard prior information. In the Helmholtz case, κ = 1/8 mm-1 (BPE) was used. (b) The mean values and standard deviations (plotted as error bars) in μa and μ´ s for different regions of breast geometry (labeled in actual image) with increasing noise level (1% to 10 %).

Fig. 3.
Fig. 3.

Photograph for gelatin phantom (representing the idealized two-dimensional cross-sectional geometry shown as first column in Fig. 4(a)) used in the experimental studies.

Fig. 4.
Fig. 4.

(a) Actual μa and μ´ s distributions (axial cross-section) of phantom (Fig. 3) case are shown in the first column. Optical properties for the region labeled ‘0’ are: μa = 0.0065 mm-1 and μ´ s = 0. 65 mm-1. Region ‘1’ values are: μa = 0.01 mm-1 and μ´ s = 1.0 mm-1. Region ‘2’ (tumor) values are: μa = 0.02 mm-1 and μ´ s = 1.2 mm-1. Reconstructed μa and μ´ s distribution from different techniques (discussed in Sec. 2) from the experimental phantom data. Second column of images does not use prior information. The middle rows use soft prior structural information and the last row of images were recovered with hard priors. In the Helmholtz case, κ = 1/16 mm-1 (BPE) was used. (b) Cross-sectional plots along the dotted line in the actual image (see first column of (a)) of the true and reconstructed μa and μ´ s distributions.

Fig. 5.
Fig. 5.

(a) Reconstructed μa and μ´ s images from the experimental phantom data using Helmholtz-type regularization matrix for different values of κ, which are given at the top of each column. (b) Cross-sectional plots along the dotted line of the actual images in Fig. 4(a) (first column) are shown with the data from reconstructed μa and μ´ s images in (a). The best prior estimate (BPE) case (κ = 1/16 mm-1) is also presented for comparison.

Tables (2)

Tables Icon

Table 1. Mean and standard deviation of the reconstructed (a) μa and (b) μ´ s values in different regions (labeled in first column of Fig. 1(a)) recovered with simulated data having 1% random noise and imperfect structural information defining region ‘1’ (7% reduction compared to the original segmentation). The corresponding reconstructed images are shown in Fig. 1(a)

Tables Icon

Table 2. Mean and standard deviation of the reconstructed (a) μa and (b) μ´ s values in different regions (labeled in first column of Fig. 4(a)) recovered from the experimental phantom data. The corresponding reconstructed images are shown in Fig. 4(a) and 5(a).

Equations (19)

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. D ( r ) ∇Φ ( r , ω ) + ( μ a ( r ) + c ) Φ ( r , ω ) = Q o ( r , ω )
D ( r ) = 1 3 [ μ a ( r ) + μ ' s ( r ) ]
Ω = min D , μ a { y F ( D , μ a ) 2 + λ ( D , μ a ) ( D 0 , μ a 0 ) 2 }
( J T J + λI ) ( δ D , δμ a ) = J T ( y F ( D , μ a ) ) λ [ ( D , μ a ) ( D 0 , μ a 0 ) ]
( J T J + 2 λI ) ( δ D , δμ a ) = J T ( y F ( D , μ a ) )
Ω = min D , μ a { y F ( D , μ a ) 2 + λ L [ ( D , μ a ) ( D 0 , μ a 0 ) ] 2 }
( J T J + λ L T L ) ( δ D , δμ a ) = J T ( y F ( D , μ a ) ) λ L T L [ ( D , μ a ) ( D 0 , μ a 0 ) ]
{ H D 2 H D μ a H D μ a H μ a 2 + ( λ D ) L T L 0 0 ( λ μ a ) L T L } [ δk δ μ a ] = [ ( J T ) D ( y F ( D , μ a ) ) ( J T ) μ a ( y F ( D , μ a ) ) ] [ ( λ D ) L T L ( D i 1 D 0 ) ( λ μ a ) L T L ( μ ai 1 μ a 0 ) ]
2 u ( r ) = 0
2 u ( r ) h 2 u 1 + u 2 + Nu N 2 + + u N 1 + u N = 0
u 1 N + u 2 N + + u N 2 + + u N 1 N + u N N = 0
L ij = { 0 if i and j are not in the same region 1 N if i and j are in the same region 1 if i = j
2 u ( r ) k 2 u ( r ) = 0
( 2 κ 2 ) u ( r ) h 2 u 1 + u 2 + + [ ( N + ( κh ) 2 ) ] u N 2 + + u N 1 + u N = 0
u 1 ( N + ( κh ) 2 ) + u 2 ( N + ( κh ) 2 ) + + u N 2 + + u N 1 ( N + ( κh ) 2 ) + u N ( N + ( κh ) 2 ) = 0
L ij = { 0 if i and j are not in the same region 1 N + ( κ h ) 2 if i and j are in the same region 1 if i = j
J ˜ = JR
ij = { 1 if i R L j 0 otherwise
( δ D , δμ a ) = R ( δD ˜ , δ μ a ˜ )

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