Quasi-Newton methods in optical tomographic image reconstruction

Inverse Problems

Volumn 19, Issue 2, 2003, Pages 387-409

  Klose, Alexander D ^a   Hielscher, Andreas H ^a  

^a MC8904 ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; IMAGE RECONSTRUCTION; ITERATIVE METHODS; LIGHT PROPAGATION; MEASUREMENT ERRORS; MEDICAL IMAGING; OPTICAL FIBERS; OPTICAL PROPERTIES; OPTIMIZATION; SCATTERING; TISSUE;

BIOMEDICAL IMAGING;

TOMOGRAPHY;

EID: 0037387924     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/19/2/309     Document Type: Article

References (57)

1. [Arridge95] Arridge S R and Schweiger M 1995 Photon-measurement density function: part D. Finite-element-method calculations Appl. Opt. 34 8026-37
2. [Arridge97] Arridge S R and Hebden J C 1997 Optical imaging in medicine: II. Modelling and reconstruction Phys. Med. Biol. 42 841-53
3. [Arridge98a] Arridge S R and Lionheart W 1998 Nonuniqueeness in diffusion-based optical tomography Opt. Lett. 23 882-4
4. [Arridge98b] Arridge S R and Schweiger M 1998 A gradient-based optimisation scheme for optical tomography Opt. Express 2 213-26
5. [Arridge99] Arridge S R 1999 Optical tomography in medical imaging Inverse Problems 15 R41-93
6. [Benaron94] Benaron D A, Ho D C, Spilman S D, Van Houten J P and Stevenson D K 1994 Non-recursive linear algorithms for optical imaging in diffusive media Oxygen Transport to Tissue (Adv. Exp. Med. Biol. vol 16) (New York: Plenum) pp 215-22
7. [Benaron00] Benaron D A et al 2000 Noninvasive functional imaging of human brain using light J. Cereb. Blood Flow Metab. 20 469-77
8. [Bishop97] Bishop Ch M 1997 Neural Networks for Pattern Recognition (Oxford: Clarendon)
9. [Broyden65] Broyden C G 1965 A class of methods for solving nonlinear simultaneous equations Math. Comput. 19 577-93
10. [Broyden67] Broyden C G 1967 Quasi-Newton methods and their application to function minimization Math. Comput. 21 368-81
11. [Case67] Case K M and Zweifel P F 1967 Linear Transport Theory (Reading, MA: Addison-Wesley)
12. [Chandrasekhar60] Chandrasekhar S 1960 Radiative Transfer (London: Oxford Univerity Press)
13. [Chang96] Chang J, Graber H L, Barbour R L and Aronson R 1996 Recovery of optical cross section perturbations in dense-scattering media by transport-theory-based imaging operators and steady-state simulated date Appl. Opt. 35 3963-78
14. [Colak97] Colak S B, Papaioannou D G, 't Hooft G W, van der Mark M B, Schomberg H, Paasschens J C J, Melissen J B M and van Asten N A A J 1997 Tomographic image reconstruction from optical projections in light-diffusing media Appl Opt. 36 180-213
15. [Colak99] Colak S B, van der Mark M B, 't Hooft G W, Hoogenraad J H, van der Linden E S and Kuijpers F A 1999 Clinical optical tomography and NIR spectroscopy for breast cancer detection IEEE J. Sel. Top. Quantum Electron. 5 1143-58
16. [Davidon91] Davidon W C 1991 Variable metric method for minimization SIAM J. Optim. 1 1-17
17. [Dennis77] Dennis J E and More J J 1977 Quasi-Newton methods, motivation and theory SIAM Rev. 19 46-89
18. [Dorn98] Dorn O 1998 A transport-backtransport method for optical tomography Inverse Problems 14 1107-30
19. [Fletcher70] Fletcher R 1970 A new approach to variable metric algorithms Comput. J. 13 317-22
20. [Fletcher87] Fletcher R 1987 Practical Methods of Optimization (Chichester: Wiley)
21. [Flock89a] Flock S T, Patterson M S, Wilson B C and Wyman D R 1989 Monte Carlo Modelling of light propagation in highly scattering tissue: 1. Model predictions and comparison with difusion theory IEEE Trans. Biomed. Eng. 36 1162-8
22. [Flock89b] Flock S T, Wilson B C and Patterson M S 1989 Monte Carlo Modelling of light propagation in highly scattering tissue: 2. Comparison with measurements in phantoms IEEE Trans. Biomed. Eng. 36 1169-73
23. [Goldfarb70] Goldfarb D 1970 A family of variable metric methods derived by variational means Math. Comput. 24 23-6
24. [Hanson98] Hanson K M, Cunningham G S and Saquib S S 1998 Inversion based on computational simulations Maximum Entropy and Bayesian Methods ed G J Erickson, J T Rychert and C R Smith (Dordrecht: Kluwer-Academic) pp 121-35
25. [Herman80]] Herman G T 1980 Image Reconstruction from Projections. The Fundamentals of Computerized Tomography (New York: Academic)
26. [Hielscher99] Hielscher A H, Klose A D and Hanson K M 1999 Gradient-based iterative image reconstruction scheme for time-resolved optical tomography IEEE Trans. Med. Imaging 18 261-71
27. [Hielscher01] Hielscher A H and Bartel S 2001 Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography J. Biomed. Opt. 6 183-92
28. [Jiang96] Jiang H, Paulsen K D, Österberg U L, Pogue B W and Patterson M S 1996 Optical image reconstruction using frequency-domain data: simulations and experiments J. Opt. Soc. Am. A 13 253-67
29. [Klose99] Klose A D and Hielscher A H 1999 Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer Med. Phys. 26 1698-707
30. [Klose02a] Klose A D, Netz U, Beuthan J and Hielscher A H 2002 Optical tomography using the time-independent equation of radiative transfer: part I. Forward model J. Quant. Spectrosc. Radiat. Transfer 72 691-713
31. [Klose02b] Klose A D and Hielscher A H 2002 Optical tomography using the time-independent equation of radiative transfer: part II. Inverse model J. Quant. Spectrosc. Radiat. Transfer 72 715-32
32. [Liu89] Liu D C and Nocedal J 1989 On the limited memory BFGS method for large scale optimization Math. Programme. 45 503-28
33. [Luenberger84] Luenberger D G 1984 Linear and Nonlinear Programming (Reading, MA: Addison-Wesley)
34. [Martinez00] Martinez J M 2000 Practical quasi-Newton methods for solving nonlinear systems J. Comput. Appl. Math. 124 97-121
35. [Matson97] Matson C L, Clark N, McMackin L and Fender J S 1997 Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves Appl. Opt. 36 214-20
36. [McBride01] McBride T O, Pogue B W, Jiang S, Osterberg U L, Paulsen K D and Poplack S P 2001 Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging Opt. Lett. 26 822-4
37. [Nash96] Nasb S G 1996 Linear and Nonlinear Programming (New York: McGraw-Hill)
38. [Natterer99] Natterer F 1999 Mathematical models for medical imaging Computational Radiology and Imaging: Therapy and Diagnostics (The IMA Volumes in Mathematics and its Applications) ed Ch Boergers and F Natterer (New York: Springer) pp 17-32
39. [Netz01] Netz U, Beuthan J, Capius H J, Koch H C, Klose A D and Hielscher A H 2001 Imaging of rheumatoid arthritis in finger joints by sagittal optical tomography Med. Laser Appl. 16 306-10
40. [Nocedal80] Nocedal J 1980 Updating quasi-Newton matrices with limited storage Math. Comput. 35 773-82
41. [Nocedal92] Nocedal J 1992 Theory of algorithms for unconstrained optimization Acta Numer. 1 199-242
42. [Nocedal99] Nocedal J and Wright S J 1999 Numerical Optimization (New York: Springer)
43. [OLeary95] O'Leary M A, Boas D A, Chance B and Yodh A G 1995 Experimental images of heterogeneous turbid media by frequency domain diffusing photon tomography Opt. Lett. 20 426-8
44. [Patterson91] Patterson M S, Wilson B C and Wyman R 1991 The propagation of optical radiation in tissue: I. Models of radiationtransport and their application Lasers Med. Sci. 6 155-67
45. [Paulsen95] Paulsen K D and Jiang H 1995 Spatially-varying optical property reconstruction using a finite element diffusion equation approximation Med. Phys. 22 691-701
46. [Press92] Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992 Numerical Recipes in C (New York: Cambridge University Press)
47. [Radon17] Radon J H 1917 Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten Ber. Verh. Sächs. Akad. Wiss. 69 262-77
48. [Roy01] Roy R and Sevick-Muraca E M 2001 A numerical study of gradient-based nonlinear optimization methods for contrast enhanced optical tomography Opt. Express. 9 49-65
49. [Ruggirero96] Gomes-Ruggiero M A and Kozakevich D N 1996 A numerical study on large-scale nonlinear solvers Comput. Math. Appl. 32 1-13
50. [Saquib97] Saquib S S, Hanson K M and Cunningham G S 1997 model-based image reconstruction from time-resolved diffusion data Medical Imaging. Image Processing (Proc. SPIE) vol 3034, ed K M Hanson (Bellingham, WA: SPIE Optical Engineering Press) pp 369-80
51. [Schottland93] Schottland J C, Haselgrove J C and Leigh J S 1993 Photon hitting density Appl. Opt. 32 448-53
52. [Schweiger99] Schweiger M and Arridge S R 1999 Application of temporal filters to time resolved data in optical tomography Phys. Med. Biol. 44 1699-717
53. [Shanno70] Shanno D 1970 Conditioning of quasi-Newton methods for function minimization Math. Comput. 24 647-57
54. [Shanno78] Shanno D 1978 Conjugate gradient methods with inexact searches Math. Oper. Res. 3 244-56
55. [Xu02] Xu Y, Gu X, Khan T and Jiang H 2002 Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data Appl. Opt. 41 5427-37
56. [Yao97] Yao Y Q, Wang Y, Pei Y L, Zhu W W and Barbour R L 1997 Frequency-domain optical imaging of absorption and scattering distributions by Born iterative method J. Opt. Soc. Am. A 14 325-42
57. [Ye99] Ye J C, Webb K J, Millane R P and Downar T J 1999 Modified distorted Born iterative method with an approximate Frechet derivative for optical tomography J. Opt. Soc. Am. A 16 1814-26