Summary
The problem of reconstructing images from measurements at the boundary of a domain belongs to the class of inverse problems. Although in different applications the techniques used to create the images work under different physical principles and map different physical parameters, they all share similar mathematical foundations. I will present here two mathematical approaches for image reconstruction. The first one is used to solve the so called history matching problem in the oil industry, and the second one is specially designed for the application of optical molecular imaging in biomedicine.
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
Suri, J.S., Farag, A.: Deformable Models: Theory and Biomaterial Applications, Springer, New York (2007)
Natterer, F., Wübbeling, F.: Mathematical Methods in Image Reconstruction. SIAM Monographs on Mathematical Modeling and Computation. SIAM, Philadelphia (2001)
Thomas, G. W.: Principles of Hydrocarbon Reservoir Simulation, Prentice-Hall, New Jersey (1982)
Villegas, R., Dorn, O., Moscoso, M., Kindelan, M., Mustieles, F.J.: Proceedings of the Paper C015, Society of Petroleum Engineers SPE-paper 1002911 (2006)
Villegas, R., Dorn, O., Moscoso, M., Kindelan, M.: Progress in Industrial Mathematics at ECMI 2006, vol. 12, pp. 597–602. (2006)
González-Rodríguez, P., Kindelan, M., Moscoso, M., Dorn, O.: Inverse Probl. 21, 565–590 (2005)
O’Leary, M.A., Boas, D.A., Li, X.D., Chance, B., Yodh, A.G.: Opt. Lett. 15, 158–160 (1996)
Hawrysz, D.J., Sevick-Muraca, E.M.: Neoplasia. 2, 388–417 (2000)
Ntziachristos, V., Weissleder, R.: Opt. Lett. 26, 893–895 (2001)
Graves, E.E., Ripoll, J., Weissleder, R., Ntziachristos, V.: Med. Phys. 30, 901–911 (2003)
Moscoso, M., Keller, J.B., Papanicolaou, G.: J. Opt. Soc. Am. A. 18(4), 948–960 (2001)
Kim, A.D., Keller, J.B.: J. Opt. Soc. Am. A. 20, 92–98 (2003)
Kim, A.D., Moscoso, M.: J. Biomed. Opt. 10, 034015 (2005)
Kim, A.D., Moscoso, M.: Inverse Probl. 22, 23–42 (2006)
González-Rodríguez, P., Kim, A.D., Moscoso, M.: J. Opt. Soc. Am. A. 24, 3456–3466 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Moscoso, M. (2010). New Mathematical Approaches for Image Reconstruction in the Oil and Medical Industries. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-12110-4_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12109-8
Online ISBN: 978-3-642-12110-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)