Abstract

A straightforward spatial deconvolution operation is presented that seeks to invert the information-blurring property of first-order perturbation algorithms for diffuse optical tomography (DOT) image reconstruction. The method that was developed to generate these deconvolving operators, or filters, was conceptually based on the frequency-encoding process used in magnetic resonance imaging. The computation of an image-correcting filter involves the solution of a large system of linear equations, in which known true distributions and the corresponding recovered distributions are compared. Conversely, application of a filter involves only a simple matrix multiplication. Simulation results show that application of this deconvolution operation to three-dimensional DOT images reconstructed by the solution of a first-order perturbation equation (Born approximation) can yield marked enhancement of image quality. In the examples considered, use of image-correcting filters produces obvious improvements in image quality, in terms of both location and μa of the inclusions. The displacements between the true and recovered locations of an inclusion’s centroid location are as small as 1 mm, in an 83cm-diameter medium with 1.53cm-diameter inclusions, and the peak value of the recovered μa for the inclusions deviates from the true value by as little as 5%.

© 2005 Optical Society of America

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2004 (1)

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

2003 (1)

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

2002 (2)

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

2001 (3)

2000 (1)

1999 (3)

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

I. Bouchouev, V. Isakov, “Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets,” Inverse Probl. 15, R95–R115 (1999).
[CrossRef]

T. F. Coleman, Y. Li, A. Verma, “Reconstructing the unknown local volatility function,” J. Comput. Finance 2, 77–102 (1999).

1998 (1)

H. L. Graber, R. Aronson, R. L. Barbour, “Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium,” J. Opt. Soc. Am. A 15, 838–848 (1998).
[CrossRef]

1997 (1)

1995 (1)

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

1994 (1)

G. L. Zeng, G. T. Gullberg, “A backprojection filtering algorithm for a spatially varying focal length collimator,” IEEE Trans. Med. Imaging 13, 549–556 (1994).
[CrossRef] [PubMed]

1993 (1)

D. Hancock, “‘Prototyping’ the Hubble fix,” IEEE Spectrum 30, 34–39 (1993).
[CrossRef]

1988 (1)

Andronica, R.

Arif, I.

Aronson, R.

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. L. Graber, R. Aronson, R. L. Barbour, “Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium,” J. Opt. Soc. Am. A 15, 838–848 (1998).
[CrossRef]

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

Barbour, R. L.

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

Y. Pei, H. L. Graber, R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging,” Appl. Opt. 40, 5755–5769 (2001).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, R. Aronson, R. L. Barbour, “Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium,” J. Opt. Soc. Am. A 15, 838–848 (1998).
[CrossRef]

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

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

H. L. Graber, R. L. Barbour, Y. Pei, “Quantification and enhancement of image reconstruction accuracy by frequency encoding of spatial information,” in Biomedical Topical Meetings, Vol. 71 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 635–637.

R. L. Barbour, H. L. Graber, Y. Pei, “A method for frequency encoded spatial filtering to enhance imaging quality of scattering media,” U.S. provisional patent application 60/309,572 (filed 2August2002).

R. L. Barbour, H. L. Graber, Y. Pei, Y. Xu, “Image enhancement by spatial linear deconvolution,” U.S. provisional patent application 60/488,325 (filed 18July2003).

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

Barbour, S. S.

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

Barbour, S.-L. S.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

Blattman, S.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

Blattman, S. B.

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

Bluestone, A.

Bouchouev, I.

I. Bouchouev, V. Isakov, “Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets,” Inverse Probl. 15, R95–R115 (1999).
[CrossRef]

Byrne, J. V.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Chang, J.

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

Coleman, T. F.

T. F. Coleman, Y. Li, A. Verma, “Reconstructing the unknown local volatility function,” J. Comput. Finance 2, 77–102 (1999).

Cox, T. C.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, “Imaging in the presence of randomly inhomogeneous media,” in Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

Graber, H. L.

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

Y. Pei, H. L. Graber, R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging,” Appl. Opt. 40, 5755–5769 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, R. Aronson, R. L. Barbour, “Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium,” J. Opt. Soc. Am. A 15, 838–848 (1998).
[CrossRef]

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

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

H. L. Graber, R. L. Barbour, Y. Pei, “Quantification and enhancement of image reconstruction accuracy by frequency encoding of spatial information,” in Biomedical Topical Meetings, Vol. 71 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 635–637.

R. L. Barbour, H. L. Graber, Y. Pei, Y. Xu, “Image enhancement by spatial linear deconvolution,” U.S. provisional patent application 60/488,325 (filed 18July2003).

R. L. Barbour, H. L. Graber, Y. Pei, “A method for frequency encoded spatial filtering to enhance imaging quality of scattering media,” U.S. provisional patent application 60/309,572 (filed 2August2002).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

Greenbaum, A.

A. Greenbaum, Iterative Methods for Solving Linear Systems (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1997), Section 3.5.1, pp. 13–16.

Gullberg, G. T.

G. L. Zeng, G. T. Gullberg, “A backprojection filtering algorithm for a spatially varying focal length collimator,” IEEE Trans. Med. Imaging 13, 549–556 (1994).
[CrossRef] [PubMed]

Hancock, D.

D. Hancock, “‘Prototyping’ the Hubble fix,” IEEE Spectrum 30, 34–39 (1993).
[CrossRef]

Hawkes, D. J.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Hielscher, A. H.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

Hipwell, J. P.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Hira, J.

Isakov, V.

I. Bouchouev, V. Isakov, “Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets,” Inverse Probl. 15, R95–R115 (1999).
[CrossRef]

Jacques, S. L.

Johnston, D. K.

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

Koo, P. C.

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

Landis, G. S.

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

Lasker, J. M.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

Li, Y.

T. F. Coleman, Y. Li, A. Verma, “Reconstructing the unknown local volatility function,” J. Comput. Finance 2, 77–102 (1999).

Löcker, M.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

Luo, H.

Matson, C. L.

Mayhew, J. E.

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

McBride, T. O.

McLaughlin, R. A.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Noble, J. A.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Österberg, U.

Ostermeyer, M. R.

Panetta, T.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

Panetta, T. F.

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

Paulsen, K. D.

Pei, Y.

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

Y. Pei, H. L. Graber, R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging,” Appl. Opt. 40, 5755–5769 (2001).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, R. L. Barbour, Y. Pei, “Quantification and enhancement of image reconstruction accuracy by frequency encoding of spatial information,” in Biomedical Topical Meetings, Vol. 71 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 635–637.

R. L. Barbour, H. L. Graber, Y. Pei, “A method for frequency encoded spatial filtering to enhance imaging quality of scattering media,” U.S. provisional patent application 60/309,572 (filed 2August2002).

R. L. Barbour, H. L. Graber, Y. Pei, Y. Xu, “Image enhancement by spatial linear deconvolution,” U.S. provisional patent application 60/488,325 (filed 18July2003).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

Penney, G. P.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Pogue, B. W.

Prewitt, J.

Ramirez, N.

Rhode, K.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Schmitz, C. H.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

Soller, I.

Summers, P.

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

Suzuki, S.

Verma, A.

T. F. Coleman, Y. Li, A. Verma, “Reconstructing the unknown local volatility function,” J. Comput. Finance 2, 77–102 (1999).

Xu, Y.

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, Y. Xu, “Image enhancement by spatial linear deconvolution,” U.S. provisional patent application 60/488,325 (filed 18July2003).

Yamaguchi, S.

Zeng, G. L.

G. L. Zeng, G. T. Gullberg, “A backprojection filtering algorithm for a spatially varying focal length collimator,” IEEE Trans. Med. Imaging 13, 549–556 (1994).
[CrossRef] [PubMed]

Zheng, Y.

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

Zhong, S.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

Appl. Opt. (5)

IEEE Comput. Sci. Eng. (1)

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

IEEE Spectrum (1)

D. Hancock, “‘Prototyping’ the Hubble fix,” IEEE Spectrum 30, 34–39 (1993).
[CrossRef]

IEEE Trans. Med. Imaging (3)

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

J. P. Hipwell, G. P. Penney, R. A. McLaughlin, K. Rhode, P. Summers, T. C. Cox, J. V. Byrne, J. A. Noble, D. J. Hawkes, “Intensity-based 2-D–3-D registration of cerebral angiograms,” IEEE Trans. Med. Imaging 22, 1417–1426 (2003).
[CrossRef] [PubMed]

G. L. Zeng, G. T. Gullberg, “A backprojection filtering algorithm for a spatially varying focal length collimator,” IEEE Trans. Med. Imaging 13, 549–556 (1994).
[CrossRef] [PubMed]

Inverse Probl. (1)

I. Bouchouev, V. Isakov, “Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets,” Inverse Probl. 15, R95–R115 (1999).
[CrossRef]

J. Comput. Finance (1)

T. F. Coleman, Y. Li, A. Verma, “Reconstructing the unknown local volatility function,” J. Comput. Finance 2, 77–102 (1999).

J. Opt. Soc. Am. A (3)

Rev. Sci. Instrum. (1)

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429–439 (2002).
[CrossRef]

Transp. Theory Stat. Phys. (1)

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

Other (14)

R. L. Barbour, H. L. Graber, Y. Pei, “A method for frequency encoded spatial filtering to enhance imaging quality of scattering media,” U.S. provisional patent application 60/309,572 (filed 2August2002).

R. L. Barbour, H. L. Graber, Y. Pei, Y. Xu, “Image enhancement by spatial linear deconvolution,” U.S. provisional patent application 60/488,325 (filed 18July2003).

J. W. Goodman, “Imaging in the presence of randomly inhomogeneous media,” in Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

T. J. Schulz, B. E. Stribling, J. J. Miller, “Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope,” Opt. Express1, 355–362 (1997), www.opticsexpress.org .
[CrossRef] [PubMed]

H. Hofer, L. Chen, Y. Yoon, B. Singer, Y. Yamauchi, D. R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberrations,” Opt. Express8, 631–643 (2001), www.opticsexpress.org .
[CrossRef] [PubMed]

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Medical Imaging 2000: Physiology and Function from Multidimensional Images, C.-T. Chen, A. V. Clough, eds., Proc. SPIE3978, 364–376 (2000).
[CrossRef]

G. S. Landis, T. F. Panetta, S. B. Blattman, H. L. Graber, Y. Pei, C. H. Schmitz, R. L. Barbour, “Clinical applications of dynamic optical tomography in vascular disease,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 130–141 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

H. L. Graber, R. L. Barbour, Y. Pei, “Quantification and enhancement of image reconstruction accuracy by frequency encoding of spatial information,” in Biomedical Topical Meetings, Vol. 71 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 635–637.

Y. Pei, H. L. Graber, R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express9, 97–109 (2001), www.opticsexpress.org .
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media,” Opt. Express7, 204–209 (2000), www.opticsexpress.org .
[CrossRef] [PubMed]

A. Greenbaum, Iterative Methods for Solving Linear Systems (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1997), Section 3.5.1, pp. 13–16.

H. L. Graber, Y. Pei, R. L. Barbour, D. K. Johnston, Y. Zheng, J. E. Mayhew, “Signal source separation and localization in the analysis of dynamic near-infrared optical tomographic time series,” in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4955, 31–51 (2003).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” Proceedings of Inter-Institute Workshop on In Vivo Optical Imaging at the NIH, A. H. Gandjbakhche, ed. (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

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Figures (13)

Fig. 1
Fig. 1

(a) Spatial map of the amplitude of one selected temporal model function assigned to the absorption coefficient (μa) of a FEM mesh node located at the intersection of the horizontal and vertical lines. In this example, the mesh is an 8-cm-diameter 2D disk with homogeneous μs′ and homogeneous time-averaged μa. (b) Spatial map of the amplitude in the time series of reconstructed μa images of the same temporal frequency as that assigned to the indicated FEM mesh node in (a).

Fig. 2
Fig. 2

Three-dimensional FEM meshes and source–detector geometries used to compute and test the image deconvolution operators. (a) Hemispheric mesh containing 982 nodes and 4309 elements. (b) Curved-slab mesh containing 984 nodes and 4274 elements. Source–detector locations are marked with small white circles.

Fig. 3
Fig. 3

Heterogeneous test media used in demonstrations of the efficiency of deconvolution to improve reconstructed image accuracy. (a)–(c) Hemisphere with one inclusion; (d)–(f) hemisphere with three inclusions; (g)–(i) curved slab with three inclusions. First column [(a), (d), (g)] shows the xy projections; the second column [(b), (e), (h)] shows the xz projections; and the third column [(c), (f), (i)] shows the yz projections of the 3D test media. Numbers along the gray scales give the quantitative value of the spatially varying μa, whereas μs is homogeneous.

Fig. 4
Fig. 4

Root-mean-squared difference between the three-inclusion hemispherical medium shown in Figs. 3(d)–3(f) and the uncorrected (dashed curve) and corrected (solid curve) reconstructed images of the same target, versus the magnitude of the Tikhonov regularization parameter λ.

Fig. 5
Fig. 5

Reconstructed image of one-inclusion hemispheric test medium [see Figs. 3(a)–3(c)]. (a)–(c) Uncorrected image, which is the solution to Eq. (6); (d)–(f) corrected image obtained by applying the spatial deconvolution to the result in (a)–(c). First column [(a) and (d)] shows the xy projections; the second column [(b) and (e)] shows the xz projections; and the third column [(c)–(f)] shows the yz projections of the 3D images. Numbers along the gray scales give the quantitative value of the spatially varying μa.

Fig. 6
Fig. 6

Reconstructed image of a three-inclusion hemispheric test medium [see Figs. 3(d)–3(f)]. See caption to Fig. 5 for explanation of gray scales and of row and column assignments.

Fig. 7
Fig. 7

Reconstructed image of a three-inclusion curved-slab test medium [see Figs. 3(g)–3(i)]. See caption to Fig. 5 for explanation of gray scales and of row and column assignments.

Fig. 8
Fig. 8

Reconstructed image of three-inclusion hemispheric test medium [see Figs. 3(d)–3(f)] when detector data are corrupted with noise in the manner described in Subsection 2.C. See caption to Fig. 5 for explanation of gray scales and of row and column assignments.

Fig. 9
Fig. 9

Reconstructed image of three-inclusion curved-slab test medium [see Figs. 3(g)–3(i)] when detector data are corrupted with noise in the manner described in Subsection 2.C. See caption to Fig. 5 for explanation of gray scales and of row and column assignments.

Fig. 10
Fig. 10

Comparison of the performance of the nonlinear iterative image reconstruction algorithm and the spatial deconvolution approach. The test medium is a curved slab with three inclusions [see Figs. 3(g)–3(i)]; detector data are noise free. See caption to Fig. 5 for explanation of gray scales and of row and column assignments.

Fig. 11
Fig. 11

Plots of assigned μa(n1, t) versus μa(n2, t) (cm−1), where n1 and n2 denote two specific curved-slab FEM mesh nodes. In particular, n1 and n2 are those nodes for which the modulation frequencies are 21/2 and 51/2 Hz. (a) μa(n1, t) versus μa(n2, t) plot for Nt = 1000; enlarged round and square dots indicate first and last points in the training and calibration time series. (b) μa(n1, t) versus μa(n2, t) plot for Nt = 16, 384. As Nt increases, sampled points in μa space constitute more complete sampling.

Fig. 12
Fig. 12

Effect of the deconvolution operator applied to the reconstructed image [Figs. 6(a)–6(c)] of a three-inclusion hemispheric test medium, as a function of Nt. From left to right: results for Nt = 103, 6 × 103, 1.2 × 104, and 1.6 × 104. The top row shows the xy projections; the middle row shows the xz projections; and the bottom row shows the yz projections of the 3D images. Numbers along the gray scale give the quantitative value of the spatially varying μa.

Fig. 13
Fig. 13

Dependence of (a) condition number and (b) of the matrix X (defined in Subsection 2.A) on Nt. Solid curves, curved-slab target medium; dashed curves, hemispheric target medium.

Equations (8)

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

I = k = 1 N t j = 1 N s ( y j k - i = 1 N s f j i x i k ) 2 ,
I f j i = - 2 k = 1 N t ( y j k - l = 1 N s f j l x l k ) x i k = 0 ,
k = 1 N t y j k x i k = k = 1 N t l = 1 N s f j l x l k x i k ,             i ,     j .
· [ D ( r ) ϕ ( r ) ] - μ a ( r ) ϕ ( r ) = - δ ( r - r s ) ,             r Λ
W r · δ x = δ I r ,
δ x = W r T ( W r W r T + λ I ) - 1 δ I r .
( δ I r ) i = ( I - I 0 ) i ( I 0 ) i ( I r ) i .
y i = a i + j = 1 N s b i j x j + j = 1 N s k = j N s c i j k [ x j 1 x k 1             x j 2 x k 2                         x j N t x k N t ] T + ,

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