Inverse problem in refractive index based optical tomography

Inverse Problems

Volumn 22, Issue 4, 2006, Pages 1121-1137

  Khan, Taufiquar ^a   Thomas, Alan ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; PROBLEM SOLVING; REFRACTIVE INDEX; TOMOGRAPHY; TRANSPORT PROPERTIES;

OPTICAL TOMOGRAPHY; OPTICAL TOMOGRAPHY INVERSE PROBLEMS; RADIATIVE TRANSPORT; RADIATIVE TRANSPORT EQUATION (RTE);

INVERSE PROBLEMS;

EID: 33746309207     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/4/001     Document Type: Article

References (40)

1. Bakushinsky A B 1993 Iterative methods for nonlinear operator equations without regularity: new approach Dokl. Russ. Acad. Sci. 330 282-4
2. Adams R 1975 Sobolev Spaces (New York: Academic)
3. Arridge S R 1999 Optical tomography in medical imaging: topical review Inverse Problems 15 R41-93
4. Bakushinsky A B, Khan T and Smirnova A 2005 Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods J. Inverse Ill-Posed Problems 13 537-51
5. Banks H T and Kunisch K 2001 Estimation Techniques for Distributed Parameter Systems (Basle: Birkhauser)
6. Blaschke B, Neubauer A and Scherzer O 1997 On convergence rates for the iteratively regularized Gauss-Newton method IMA J. Numer. Anal. 17 421-36
7. O'Leary M A, Boas D A, Chance B and Yodh A G 1993 Optics for diffuse photon density waves Proc. SPIE (vol 1888) Photon Migration and Imaging in Random Media and Tissues (September 1993) ed B Chance and R R Alfano pp 334-9
8. Schweiger M and Arridge S R 1995 Near-infrared imaging: photon measurement density functions Proc. SPIE (vol 2389) Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation (May 1995) ed B Chance and R R Alfano pp 366-77
9. Daners D 2000 Robin boundary value problems on arbitrary domains Trans. Am. Math. Soc. 352 4207-36
10. Das B B, Liu F and Alfano R R 1997 Time-resolved fluorescence and photon migration studies in biomedical and model random media Rep. Prog. Phys. 60 227-92
11. Delphy D T and Cope M 1997 Quantification in tissue near-infrared spectroscopy Phil. Trans. R. Soc. B 352 649-59
12. Dierkes T, Dorn O, Natterer F, Palamodov V and Sielschott H 2002 Fréchet derivatives for some bilinear inverse problems SIAM J. Appl. Math. 62 2093-113
13. Evans L C 1998 Partial Differential Equations (Providence, RI: American Mathematical Society)
14. Folland G B 1995 Introduction to Partial Differential Equations 2nd edn (Princeton, NJ: Princeton University Press)
15. Gibson A, Hebden J and Arridge S 2005 Recent advances in diffuse optical imaging Phys. Med. Biol. 50 R1-43
16. Hanke M, Nagy J and Vogel C 2000 Quasi-Newton approach to nonnegative image restorations Linear Algebra Appl. 316 223-36
17. Hebden J, Arridge S R and Delphy D T 1997 Optical imaging in medicine: I. Experimental techniques Phys. Med. Biol. 42 825-40
18. Hielscher A, Alcouffe R and Barbour R 1998 Comparison of finite-difference transport and diffusion calculations for photon migration in homogenous and heterogenous tissues Phys. Med. Biol. 42 1285-302
19. Hohage T 1997 Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and inverse scattering problem Inverse Problems 13 1279-99
20. Jiang H, Iftimia V, Xu Y, Eggert J, Fajardo L and Klove K 2002 Near-infrared optical imaging of the breast with model-based reconstruction Acad. Radiol. 9 186-94
21. Khan T and Jiang H 2003 A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices J. Opt. A: Pure Appl. Opt. 5 137-41
22. Khan T and Smirnova A 2005 1D inverse problem in diffusion based optical tomography using iteratively regularized Gauss-Newton algorithm Appl. Math. Comput. 161 149-70
23. n or spherical harmonics approximation for scattering media with spatially varying and spatially constant refractive indices Opt. Commun. 255 130-66
24. Lai J, Li Z, Wang C and He A 2005 Experimental measurement of the refractive index of biological tissues by total internal reflection Appl. Opt. 44 1845-9
25. Li H and Xie S 1996 Measurement method of the refractive index of biotissue by total internal reflection Appl. Opt. 35 1793-5
26. Marti-Lopez L, Bouza-Dominguez J and Hebden J 2004 Interpretation of the failure of the time-dependent diffusion equation near a point source Opt. Commun. 242 23-43
27. Marti-Lopez L, Bouza-Dominguez J, Hebden J, Arridge S and Martinez-Celorio R 2003 Validity conditions for the radiative transfer equation J. Opt. Soc. Am. A 20 2046-56
28. Mathworks 2005 Matlab Reference Manual (TX, USA: Mathworks)
29. Nash S G and Sofer A 1996 Linear and Nonlinear Programming (New York: McGraw-Hill)
30. Natterer F and Wübbeling F 2001 Mathematical Methods in Image Reconstruction (SIAM Monographs on Mathematical Modeling and Computation) (Philadelphia, PA: SIAM)
31. Ohmi M, Ohnishi Y, Yoden K and Haruan M 2000 In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry IEEE Trans. Biomed. Eng. 47 1266-70
32. Pomraning G C Radiation Hydrodynamics (Oxford: Pergamon)
33. Roggermann M C, Welsh B M, Gardner P J, Johnson R L and Pedersen B L 1995 Sensing three-dimensional index-of-refraction variations by means of optical wavefront sensor measurements and tomographic reconstruction Opt. Eng., Bellingham 34 1374-84
34. Schweiger M, Arridge S and Nissilae I 2005 Gauss-Newton method for image reconstruction in diffuse optical tomography Phys. Med. Biol. 50 2365-86
35. Shendeleva M L 2004 Radiative transfer in a turbid medium with a varying refractive index: comment J. Opt. Soc. Am. A Opt. Image Sci. Vis. 21 2464-7
36. Tearney G J, Brezinski M E, Southern J F, Bouma B E, Hee M R and Fujimoto J G 1995 Determination of the refractive index of highly scattering human tissue by optical coherence tomography Opt. Lett. 20 2258-60
37. Tualle J and Tenet E 2003 Derivation of the radiative transfer equation for scattering media with spatially varying refractive index Opt. Commun. 228 33-8
38. Wloka J 1982 Partial Differential Equations (Cambridge: Cambridge University Press)
39. Xu Y, Gu X, Khan T and Jiang H 2002 Absorption and scattering image of heterogenous scattering media can be simultaneously reconstructed using dc data Appl. Opt. 41 5427-37
40. Xu Y, Iftimia N, Jiang H, Key L and Bolster M 2002 Three-dimensional diffuse optical tomography of bones and joints J. Biomed. Opt. 7 21-5