A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer

Journal of Quantitative Spectroscopy and Radiative Transfer

Volumn 104, Issue 1, 2007, Pages 24-39

  Kim, Hyun Keol ^a   Charette, André ^a  

^a UNIVERSITÉ DU QUÉBEC À CHICOUTIMI   (Canada)

Author keywords

Adjoint problem; Anisotropic scattering; Cross talk; Forward problem; Frequency domain; Inverse problem; Optical tomography; Radiative transfer equation; SFCGM

Indexed keywords

FINITE DIFFERENCE METHOD; FREQUENCY DOMAIN ANALYSIS; GRADIENT METHODS; INVERSE PROBLEMS; MEDICAL IMAGING; OPTIMIZATION; SENSITIVITY ANALYSIS; TOMOGRAPHY;

ANISOTROPIC SCATTERING; OPTICAL TOMOGRAPHY; RADIATIVE TRANSFER EQUATION; SCATTERING COEFFICIENTS; SENSITIVITY FUNCTION-BASED CONJUGATE GRADIENT METHOD;

HEAT RADIATION;

ABSORPTION SPECTRUM; FINITE DIFFERENCE METHOD; GRADIENT ANALYSIS; INVERSE PROBLEM; OPTIMIZATION; RADIATIVE TRANSFER; SENSITIVITY ANALYSIS; TOMOGRAPHY;

EID: 33750515705     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2006.08.007     Document Type: Article

References (48)

1. Xu Y., Iftimia N., Jiang H., Lyndon-Key L., and Bolster M.B. Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography. Opt Express 8 (2001) 447-451
2. Bluestone A.Y., Abdoulaev G., Schmitz C.H., Barbour R.L., and Hielscher A.H. Three-dimensional optical tomography of hemodynamics in the human head. Opt Express 9 (2001) 272-286
3. Nioka S., Yung Y., Shnall M., Zhao S., Orel S., Xie C., et al. Optical imaging of breast tumor by means of continuous waves. Adv Exp Med Biol 411 (1997) 227-232
4. Wells K., Hebden J.C., Schmidt F.E.W., and Delpy D.T. The UCL multichannel time-resolved system for optical tomography. Proc SPIE 2979 (1997) 599-607
5. Fantini S., Franceschini M.A., Maier J.S., Walker S.A., Barbieri B., and Gratton E. Frequency domain multi-channel optical detector for noninvasive tissue spectroscopy and oximetry. Opt Eng 34 (1995) 32-42
6. Barbour R.L., Graber H.L., Chang J.W., Barbour S.L.S., Koo P.C., and Aronson R. MRI-guided optical tomography: prospects and computation for a new imaging method. IEEE Comput Sci Eng 2 (1995) 63-77
7. Yao Y.Q., Wang Y., Pei Y.L., Zhu W.W., and Barbour R.L. Frequency-domain optical imaging of absorption and scattering distributions by Born iterative method. J Opt Soc Am A 14 (1997) 325-342
8. O'Leary M.A., Boas D.A., Chance B., and Yodh A.G. Experimental images of heterogeneous turbid media by frequency-domain diffusion photon tomography. Opt Lett 20 (1995) 426-428
9. Chang J., Zhu W., Wang Y., Graber H., and Barbour R.L. Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data. J Opt Soc Am A 14 (1997) 306-312
10. Arridge S.R. Photon-measurement density functions. Part I: analytical forms. Appl Opt 34 (1995) 7395-7409
11. Arridge S.R., and Schweiger M. Photon measurement density functions. Part 2: finite-element-method calculation. Appl Opt 34 (1995) 8026-8037
12. Paulsen K.D., and Jiang H. Spatially varying optical property reconstruction using a finite element diffusion equation approximation. Med Phys 22 (1995) 691-701
13. Paulsen K.D., and Jiang H. Enhanced frequency domain optical image reconstruction in tissues through total variation minimization. Appl Opt 35 (1996) 3447-3458
14. Jiang H., Paulsen K.D., and Osterberg U.L. Optical image reconstruction using DC data: simulations and experiments. Phys Med Biol 41 (1996) 1483-1498
15. Jiang H., Paulsen K.D., Osterberg U.L., Pogue B.W., and Patterson M.S. Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data. Opt Lett 20 (1995) 2128-2130
16. Patterson M.S. Optical image reconstruction using frequency domain data: simulations and experiments. J Opt Soc Am A 13 (1996) 253-266
17. Klose A.D., and Hielscher A.H. Quasi-newton methods in optical tomographic image reconstruction. Inverse Problems 19 (2003) 309-387
18. Hielscher A.H., Klose A.D., and Hanson K.M. Gradient-based iterative image reconstruction scheme for time-resolved optical tomography. IEEE Trans Med Imaging 18 (1999) 262-271
19. Roy R., and Sevick-Muraca E.M. Truncated Newton's optimization scheme for absorption and fluorescence optical tomography. Part I: theory and formulation. Opt Express 4 (1999) 353-371
20. Saquib S.S., Hanson K.M., and Cunningham G.S. Model-based image reconstruction from time-resolved diffusion data. Proc SPIE 3034 (1997) 369-380
21. Arridge S.R., and Schweiger M. A gradient-based optimisation scheme for optical tomography. Opt Express 2 (1998) 213-226
22. Arridge S.R., and Hebden J.C. Optical imaging in medicine: II Modelling and reconstruction. Phys Med Biol 42 (1997) 841-853
23. Hielscher A.H., Alcouffe A.E., and Barbour R.L. Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. Phys Med Biol 43 (1998) 1285-1302
24. Firbank M., Arridge S.R., Schweiger M., and Delpy D.T. An investigation of light transport through scattering bodies with non-scattering regions. Phys Med Biol 41 (1996) 767-783
25. Sakami M., Mitra K., and Hsu P.F. Analysis of light pulse transport through two-dimensional scattering and absorbing media. JQSRT 73 (2002) 169-179
26. Francoeur M., Vaillon R., and Rouse D.R. Theoretical analysis of frequency and time-domain methods for optical characterization of absorbing and scattering media. JQSRT 93 (2005) 139-150
27. Sakami M, Mitra K, Hsu PF. Transient radiative transfer in aniostropically scattering media using monotonicity-preserving schemes. ASME-HTD-366-1 international ME congress and exposition, Orlando, FL, 2000. p. 135-143.
28. Klose A.D., and Hielscher A.H. Optical tomography using the time-independent equation of radiative transfer-part 2: inverse model. JQSRT 72 (2002) 715-732
29. Klose A.D., and Hielsher A.H. Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer. Med Phys 26 (1999) 1698-1707
30. Boulanger J., and Charette A. Numerical developments for short-pulsed near infra-red spectroscopy. Part I: direct treatment. JQSRT 91 (2005) 189-209
31. Boulanger J., and Charette A. Numerical developments for short-pulsed near infra-red spectroscopy. Part II: inverse treatment. JQSRT 91 (2005) 297-318
32. Boulanger J, Charette A, Liu F. Modulation frequency analysis of 1-D semi-transparent medium, Proceedings of IMECE 2004 ASME international mechanical engineering congress and R & D expo, Anaheim, CA, USA, November 13-19, 2004.
33. Ren K., Abdoulaev G.S., Bal G., and Hielsher A.H. Algorithm for solving the equation of radiative transfer in the frequency domain. Opt Lett 29 (2004) 578-580
34. Ren K, Hielsher AH, Frequency domain optical tomography based on the equation of radiative transfer, http://www.columbia.edu/~gb2030/PAPERS/FRERT.pdf.
35. Abdoulaev G., Ren K., and Hielsher A. Optical tomography as a PDE-constrained optimization problem. Inverse Problems 21 (2005) 1507-1530
36. Artyukhin E.A., and Rumjantsev S.V. Optimal choice of descent steps in gradient methods of solution of inverse heat conduction problems. J Eng Phys 39 (1980) 865-869
37. Beck B.V., and Arnold K.J. Parameter estimation in engineering and science (1987), Wiley Interscience, New York
38. Alifanov O.M. Inverse heat transfer problems (1994), Springer, Berlin
39. Li H.Y., and Ozisik M.N. Inverse radiation problem for simultaneous estimation of temperature profile and surface reflectivity. J Thermophys Heat Transf 7 (1993) 88-93
40. Ustinov E.A. Adjoint sensitivity analysis of radiative transfer equation: 2. Applications to retrievals of temperature in scattering atmospheres in thermal IR. JQSRT 73 (2002) 29-40
41. Arridge S. Optical tomography in medical imaging. Inverse Problems 15 (1999) R41-R93
42. Modest M. Radiative heat transfer (1993), MacGraw-Hill Inc, New York
43. Mishchenko M.I., Lucis A.A., and Travis L.D. Errors induced by the neglect of polarization in radiance calculations for rayleigh-scattering atmostpheres. JQSRT 51 (1994) 491-510
44. Lewis E.E., and Miller W.F. Computational methods of neutron transport (1984), Wiley, New York
45. Box M.A., Gerstl S.A.W., and Simmer C. Application of the adjoint formulation to the calculation of atmospheric radiative effects. Beitr Phys Atmosph 61 (1988) 303-311
46. Polonsky I.N., Box M.A., and Davis A.B. Radiative transfer through inhomogeneous turbid media: implementation of the adjoint perturbation approach at the 1st order. JQSRT 78 (2003) 85-98
47. Dai Y.H. Convergence of nonlinear conjugate gradient methods. J Comput Math 19 (2001) 539-548
48. Kim HK, Charette A. A new solution method for optical tomography in the frequency domain. Proceedings of the 13th international heat transfer conference, Sydney, Australia, 13-18 August, 2006.