Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography

Medical Physics

Volumn 34, Issue 6, 2007, Pages 2085-2098

  Yalavarthy, Phaneendra K ^a   Pogue, Brian W ^a   Dehghani, Hamid ^b   Paulsen, Keith D ^a  

^a DARTMOUTH COLLEGE   (United States)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Diffuse optical tomography; Inverse problems; Least squares minimization; Near infrared

Indexed keywords

IMAGE RECONSTRUCTION; INFRARED DEVICES; INVERSE PROBLEMS; MATRIX ALGEBRA; OPTICAL PROPERTIES; OPTICAL TOMOGRAPHY; SIGNAL TO NOISE RATIO;

DIFFUSE OPTICAL TOMOGRAPHY; GENERALIZED LEAST SQUARE; LEAST SQUARES MINIMIZATION; LEAST SQUARES TECHNIQUES; NEAR INFRARED; OPTIMAL REGULARIZATION METHODS; RECONSTRUCTION PROCEDURE; TISSUE OPTICAL PROPERTIES;

LEAST SQUARES APPROXIMATIONS;

ARTICLE; IMAGING; MATHEMATICAL ANALYSIS; METHODOLOGY; NOISE; OPTICAL TOMOGRAPHY; PRIORITY JOURNAL; SPATIAL DISCRIMINATION;

EID: 34250854093     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.2733803     Document Type: Article

References (65)

1. A. Gibson, J. C. Hebden, and S. R. Arridge, " Recent advances in diffuse optical tomography., " Phys. Med. Biol. 50, R1-R43 (2005).
2. S. R. Arridge, " Optical tomography in medical imaging., " Inverse Probl. 15, R41-R93 (1999).
3. S. R. Arridge and J. C. Hebden, " Optical imaging in medicine: II. Modelling and reconstruction., " Phys. Med. Biol. 42, 841-853 (1997).
4. S. R. Arridge and M. Schweiger, in " A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method., " The IMA Volumes in Mathematics and Its Applications: Computational Radiology and Imaging, Therapy and Diagnostics, edited by, F. N. C. Börgers, (Springer, New York, 1998), pp. 45-70.
5. M. Schweiger, S. R. Arridge, and I. Nissila, " Gauss-Newton method for image reconstruction in diffuse optical tomography., " Phys. Med. Biol. 50, 2365-2386 (2005).
6. 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, 57-75 (2001).
7. 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).
8. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, " Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography., " Proc. Natl. Acad. Sci. U.S.A. 100, 12349-12354 (2003).
9. 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 Comput. Sci. Eng. 2, 63-77 (1995).
10. B. W. Pogue and K. D. Paulsen, " High-resolution near-infrared tomographic imaging simulations of the rat cranium by use of a priori magnetic resonance imaging structural information., " Opt. Lett. 23, 1716-1718 (1998).
11. 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).
12. J. P. Kaipio, V. Kolehmanien, M. Vauhkonen, and E. Somersalo, " Inverse problems with structural prior information., " Inverse Probl. 15, 713-729 (1999).
13. M. Schweiger and S. R. Arridge, " Optical tomographic reconstruction in a complex head model using a priori region boundary information., " Phys. Med. Biol. 44, 2703-2721 (1999).
14. V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, " Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement., " Proc. Natl. Acad. Sci. U.S.A. 97, 2767-2772 (2000).
15. 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).
16. 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).
17. 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).
18. 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).
19. 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).
20. X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, " Diffuse optical tomography with physiological and spatial a priori constraints., " Phys. Med. Biol. 49, N155-N163 (2004).
21. 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).
22. 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, 024033:1-024033:9 (2005).
23. 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).
24. M. Guven, B. Yazici, X. Intes, and B. Chance, " Diffuse optical tomography with a priori anatomical information., " Phys. Med. Biol. 50, 2837-2858 (2005).
25. 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. Natl. Acad. Sci. U.S.A. 103, 8828-8833 (2006).
26. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, S. Jiang, and K. D. Paulsen, " Structural information within regularization matrices improves near infrared diffuse optical tomography. " (unpublished).
27. A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, " Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information., " Meas. Sci. Technol. 18, 87-95 (2007).
28. H. Jiang, K. D. Paulsen, and 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).
29. 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).
30. S. R. Arridge and M. Schweiger, " Photon-measurement density functions. Part 2: Finite-element-method calculations., " Appl. Opt. 34, 8026-8037 (1995).
31. 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).
32. H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, " The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach., " Phys. Med. Biol. 48, 2713-2727 (2003).
33. S. R. Arridge and M. Schweiger, " A gradient based optimization scheme for optical tomography., " Opt. Express 2, 213-226 (1998).
34. A. H. Hielscher, A. D. Klose, and K. M. Hanson, " Gradient-based iterative image reconstruction scheme for time-resolved optical tomography., " IEEE Trans. Med. Imaging 18, 262-271 (1999).
35. K. D. Paulsen and H. Jiang, " Enhanced frequency domain optical image reconstruction in tissues through variation minimization., " Appl. Opt. 35, 3447-3458 (1996).
36. J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Milane, " Nonlinear multigrid algorithms for Bayesian optical diffusion tomography., " IEEE Trans. Image Process. 10, 909-922 (2001).
37. M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, and E. M. Sevick-Muraca, " Three-dimensional Bayesian optical image reconstruction with domain decomposition., " IEEE Trans. Med. Imaging 20, 147-163 (2001).
38. V. Kolehmainen, " Novel approaches to image reconstruction in diffusion tomography., " Ph.D. thesis, Kuopio University, Finland, 2001.
39. M. S. Zhdanov, Geophysical Inverse Theory and Regularization Problems, 1st ed. (Elsevier Science, New York, 2002).
40. K. Levenberg, " A method for the solution of certain nonlinear problems in least squares., " Proc. Soc. Exp. Stress Anal. 2, 164-168 (1944).
41. D. W. Marquardt, " An algorithm for least squares estimation of nonlinear parameters., " J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
42. M. Schweiger, S. R. Arridge, and D. T. Delpy, " Application of the finite element method for the forward and inverse models in optical tomography., " J. Math. Imaging Vision 3, 263-283 (1993).
43. A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston and Sons, Washington, 1977).
44. A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2004).
45. 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).
46. 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).
47. D. R. Lynch, Numerical Partial Differential Equations for Environmental Scientists and Engineers-A First Practical Course (Springer, New York, 2005).
48. P. K. Yalavarthy and D. R. Lynch, " Generalized least-squares minimization for diffuse optical tomography: Use of complex data., " NML Lab Report, NML-06-9, Dartmouth College, 2006, http://www-nml.dartmouth.edu/ Publications/internal_reports/NML-06-9/.
49. B. Brandstter, K. Hollaus, H. Hutten, M. Mayer, R. Merwa, and H. Scharfetter, " Direct estimation of Cole parameters in multifrequency EIT using a regularized Gauss-Newton method., " Physiol. Meas 24, 437-448 (2003).
50. N. Soni, K. D. Paulsen, H. Dehghani, and A. Hartov, " Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography., " IEEE Trans. Med. Imaging 25, 55-61 (2006).
51. A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, " In vivo absorption, scattering and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy., " J. Biomed. Opt. 11, 044005 (2006).
52. V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, " Quantification of optical properties of a breast tumor using random walk theory., " J. Biomed. Opt. 7, 80-87 (2002).
53. 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).
54. 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).
55. B. W. Pogue, X. Song, T. D. Tosteson, T. O. McBride, S. Jiang and K. D. Paulsen, " Statistical analysis of non-linearly reconstructed near-infrared tomographic images: Part I-Theory and simulations., " IEEE Trans. Med. Imaging 21, 755-763 (2002).
56. X. Song, B. W. Pogue, T. D. Tosteson, T. O. McBride, S. Jiang, and K. D. Paulsen, " Statistical analysis of non-linearly reconstructed near-infrared tomographic images: Part II-Experimental interpretation., " IEEE Trans. Med. Imaging 21, 764-772 (2002).
57. T. O. Mcbride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, " A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo., " Rev. Sci. Instrum. 72, 1817-1824 (2001).
58. 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).
59. B. M. Graham and A. Adler, " Objective selection of hyperparameter for EIT., " Physiol. Meas 27, S65-S79 (2006).
60. 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.
61. P. C. Hansen, " Analysis of discrete ill-posed problems by means of the L -curve., " SIAM Rev. 34, 561-581 (1992).
62. 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).
63. http://nir.thayer.dartmouth.edu/lscomparison.html.
64. P. K. Yalavarthy, " Diffuse optical tomographic reconstruction in low-scattering tissue: Development of inversion algorithms based on Monte-Carlo simulation., " M.Sc.(Engg.) thesis, Indian Institute of Science, Bangalore, India, 2004.
65. M. Fedi, P. C. Hansen, and V. Paoletti, " Analysis of depth resolution in potential-field inversion., " Geophysics 70, A1-A11 (2005).