We introduce a modified Tikhonov regularization method to include three-dimensional x-ray mammography as a prior in the diffuse optical tomography reconstruction. With simulations we show that the optical image reconstruction resolution and contrast are improved by implementing this x-ray-guided spatial constraint. We suggest an approach to find the optimal regularization parameters. The presented preliminary clinical result indicates the utility of the method.

© 2003 Optical Society of America

1. A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
2. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
3. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18 (6), 57–75 (2001).
4. Y. Hoshi and M. Tamura, “Near-infrared optical detection of sequential brain activation in the prefrontal cortex during mental tasks,” Neuroimage 5, 292–297 (1997).
5. A. Maki, Y. Yamashita, E. Watanabe, and H. Koizumi, “Visualizing human motor activity by using non-invasive optical topography,” Front. Med. Biol. Eng. 7, 285–297 (1996).
6. B. Chance, A. Endla, N. Shoko, Z. Shuoming, H. Long, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, “A novel method for fast imaging of brain function, non-invasively, with light,” Opt. Express 2, 411–423 (1998), http://www.opticsexpress.org
7. M. A. Franceschini, V. Toronov, M. Filiaci, E. Gratton, and S. Fanini, “On-line optical imaging of the human brain with 160-ms temporal resolution,” Opt. Express 6, 49–57 (2000), http://www.opticsexpress.org.
8. S. R. Hintz, D. A. Benaron, A. M. Siegel, A. Zourabian, D. K. Stevenson, and D. A. Boas, “Bedside functional imaging of the premature infant brain during passive motor activation,” J. Perinat. Med. 29, 335–343 (2001).
9. J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
10. R. L. Barbour, H. L. Graber, J. Chang, S. S. Barbour, P. C. Koo, and R. Aronson, ““MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).
11. V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “MRI-guided diffuse optical spectroscopy of malignant and benign breast lesions,” Neoplasia 4, 347–354 (2002).
12. Q. Zhu, T. Durduran, V. Ntziachristos, M. Holboke, and A. G. Yodh, “Imager that combines near-infrared diffusive light and ultrasound,” Opt. Lett. 24, 1050–1052 (1999).
13. M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. dissertation (Department of Physics, Unversity of Pennsylvania, Philadelphia, Pa., 1996).
14. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
15. O. Arikan, “Regularized inversion of a two-dimensional integral equation with applications in borehole induction measurements,” Radio Sci. 29, 519–538 (1994).
16. M. Belge, M. Kilmer, and L. E. Miller, “Efficient determination of multiple regularization parameters in a generalized L-curve framework,” Inverse Probl. 18, 1161–1183 (2002).
17. S. R. Arridge and M. Schweiger, “Inverse methods for optical tomography,” in Proceedings of Information Processing in Medical Imaging (IPMI’93), H. H. Barrett and A. F. Gmitro, eds., Vol. 687 of Lecture Notes in Computer Science, (Springer-Verlag, New York, 1993).
18. S. R. Arridge, “Photo-measurement density functions. Part I: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
19. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation (Department of Physics, University of Pennsylvania, Philadelphia, Pa., 1996).
20. 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).
21. Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, and D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, Proc. SPIE 4250, 219–238 (2001).
22. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM Press, Philadelphia, Pa., 1998).
23. J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
24. L. T. Niklason, B. T. Christian, L. E. Niklason, D. B. Kopans, D. E. Castleberry, B. H. Opsahl-Ong, C. E. Landberg, P. J. Slanetz, A. A. Giardino, R. Moore, D. Albagli, M. C. DeJule, P. E. Fitzgerald, D. F. Fobare, B. W. Giambattista, R. F. Kwasnick, J. Liu, S. J. Lubowski, G. E. Possin, J. F. Richotte, C.-Y. Wei, and R. F. Wirth, “Digital tomosynthesis in breast imaging,” Radiology 205, 399–406 (1997).
25. T. Wu, “Three dimensional mammography reconstruction using low dose projection images, Ph. D. dissertation (Department of Physics, Brandeis University, Waltham, Mass., 2002).
26. M. J. D. Eppstein, D. E. Troy, T. L. Troy, and E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).

Appl. Opt.

• B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
• S. R. Arridge, “Photo-measurement density functions. Part I: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
• M. J. D. Eppstein, D. E. Troy, T. L. Troy, and E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).

Front. Med. Biol. Eng.

• A. Maki, Y. Yamashita, E. Watanabe, and H. Koizumi, “Visualizing human motor activity by using non-invasive optical topography,” Front. Med. Biol. Eng. 7, 285–297 (1996).

IEEE Comput. Sci. Eng.

• R. L. Barbour, H. L. Graber, J. Chang, S. S. Barbour, P. C. Koo, and R. Aronson, ““MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

IEEE Signal Process. Mag.

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

Inverse Probl.

• S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
• M. Belge, M. Kilmer, and L. E. Miller, “Efficient determination of multiple regularization parameters in a generalized L-curve framework,” Inverse Probl. 18, 1161–1183 (2002).

J. Perinat. Med.

• S. R. Hintz, D. A. Benaron, A. M. Siegel, A. Zourabian, D. K. Stevenson, and D. A. Boas, “Bedside functional imaging of the premature infant brain during passive motor activation,” J. Perinat. Med. 29, 335–343 (2001).

Med. Phys.

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

Neoplasia

• V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “MRI-guided diffuse optical spectroscopy of malignant and benign breast lesions,” Neoplasia 4, 347–354 (2002).

Neuroimage

• Y. Hoshi and M. Tamura, “Near-infrared optical detection of sequential brain activation in the prefrontal cortex during mental tasks,” Neuroimage 5, 292–297 (1997).

Opt. Express

• B. Chance, A. Endla, N. Shoko, Z. Shuoming, H. Long, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, “A novel method for fast imaging of brain function, non-invasively, with light,” Opt. Express 2, 411–423 (1998), http://www.opticsexpress.org
• M. A. Franceschini, V. Toronov, M. Filiaci, E. Gratton, and S. Fanini, “On-line optical imaging of the human brain with 160-ms temporal resolution,” Opt. Express 6, 49–57 (2000), http://www.opticsexpress.org.

Opt. Lett.

• J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
• Q. Zhu, T. Durduran, V. Ntziachristos, M. Holboke, and A. G. Yodh, “Imager that combines near-infrared diffusive light and ultrasound,” Opt. Lett. 24, 1050–1052 (1999).

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).

Phys. Today

• A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).

Radio Sci.

• O. Arikan, “Regularized inversion of a two-dimensional integral equation with applications in borehole induction measurements,” Radio Sci. 29, 519–538 (1994).

Radiology

• L. T. Niklason, B. T. Christian, L. E. Niklason, D. B. Kopans, D. E. Castleberry, B. H. Opsahl-Ong, C. E. Landberg, P. J. Slanetz, A. A. Giardino, R. Moore, D. Albagli, M. C. DeJule, P. E. Fitzgerald, D. F. Fobare, B. W. Giambattista, R. F. Kwasnick, J. Liu, S. J. Lubowski, G. E. Possin, J. F. Richotte, C.-Y. Wei, and R. F. Wirth, “Digital tomosynthesis in breast imaging,” Radiology 205, 399–406 (1997).

Other

• T. Wu, “Three dimensional mammography reconstruction using low dose projection images, Ph. D. dissertation (Department of Physics, Brandeis University, Waltham, Mass., 2002).
• Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, and D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, Proc. SPIE 4250, 219–238 (2001).
• P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM Press, Philadelphia, Pa., 1998).
• D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation (Department of Physics, University of Pennsylvania, Philadelphia, Pa., 1996).
• S. R. Arridge and M. Schweiger, “Inverse methods for optical tomography,” in Proceedings of Information Processing in Medical Imaging (IPMI’93), H. H. Barrett and A. F. Gmitro, eds., Vol. 687 of Lecture Notes in Computer Science, (Springer-Verlag, New York, 1993).
• M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. dissertation (Department of Physics, Unversity of Pennsylvania, Philadelphia, Pa., 1996).

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