Abstract
The authors have recently introduced a novel imaging algorithm for optical/diffusion tomography, the “Elliptic Systems Method” (ESM). In this article the performance of the ESM is analyzed for experimental data. Images are obtained for the case of a single source and seven (7) detector locations, an unusually limited number of source/detector pairs. These images are verified by numerical simulation. A new approach to data fitting (at the detectors) is introduced.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Arridge and M. Schweiger, 1995, Sensitivity to prior knowledge in optical tomographic reconstruction,Proc. of SPIE, 2389,378–388 (SPIE - The Society of Photo-Optical Instrumentation Engineers).
R. Barbour, H. Grader, J. Chang, S. Barbour, S. Koo, and R. Aronson, 1995, MRI-guided optical tomography, IEEE Comp. Sci. Eng., 2,#4, 63–77.
W. Cai, B. Das, F. Liu, M. Zevallos, M. Lax, and R. Alfano, 1997, Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,Proc. Natl. Acad. Sci. USA, 93,13561–13564.
K. Case and P. Zweifel, 1967, Linear Transport Theory,Addison-Wiley Publishing Company, London.
S. Colak, D. Papaioannou, G. Hooft, M. Van den Mark, H. Schomberg, J. Paasschens, J. Melissen, and N. Van Asten, 1997, Tomographie image reconstruction from optical projections in light-diffusing media,Applied Optics, 36,180–213.
M. Klibanov and F. Santosa, 1991, Computational quasi-reversibility method for Cauchy problems for Laplace’s equation,SIAM J. Appl. Math., 51,1655–1675.
M. Klibanov and Rakesh, 1992, Numerical solution of a time-like Cauchy problem for the wave equation,Math. Methods in Appl. Sci., 15,559–580.
M. Klibanov, T. Lucas, and R. Frank, 1997, A fast and accurate imaging algorithm in optical/diffusion tomography, Inverse Problems, 13,1341–1361.
O. Ladyzenskaya, V. Solonnikov, and N. Uralceva, 1968, Linear and Quasi-linear Equations of Parabolic Type, AMS, Providence, RI.
M. Lavrentiev, V. Romanov, and S. Shishatskii, 1986, Ill-Posed Problems Of Mathematical Physics And Analysis,AMS, Providence, RI.
R. Lattes and J.-L. Lions, 1969, Method of Quasi-Reversibility: Applications To Partial Differential Equations, Elsevier, New York.
Mathematics and Physics of Emerging Biomedical Imaging,1996, National Research Council, Institute of Medicine, National Academic Press, Washington, D.C.
M. O’Leary, D. Boas, B. Chance, and A. Yodh, 1994, Images of inhomogeneous turbid media using diffuse photon density waves, in Optical Society of America Proc. “Advances In Optical Imaging And Photon Migration,” 21, 106–115.
V. Romanov, 1987, Inverse Problems of Mathematical Physics,VNU Press, Uthrecht.
L. Souriau, B. DuchÊne, D. Lesselier, and R. Kleinman, 1996, Modified gradient approach to inverse scattering for binary objects in stratified media,Inverse Problems, 12,463–481.
A. Wolbrast, 1993, Physics of Radiology,Appleton & Lange, Norwalk, CT.
V. Yakhno, 1990, Inverse Problems for Differential Equations of Elasticity, Novosibirsk, Nauka (in Russian).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Klibanov, M.V., Lucas, T.R., Frank, R.M. (1999). Image Reconstruction from Experimental Data in Diffusion Tomography. In: Börgers, C., Natterer, F. (eds) Computational Radiology and Imaging. The IMA Volumes in Mathematics and its Applications, vol 110. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1550-9_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1550-9_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7189-5
Online ISBN: 978-1-4612-1550-9
eBook Packages: Springer Book Archive