Statistical model for tomographic reconstruction methods using spline functions

Habib Benali; Jeanpierre V. Guedon; Irene Buvat; Melanie Pelegrini; Yves J. Bizais; Robert Di Paola

doi:10.1117/12.179255

8 July 1994 Statistical model for tomographic reconstruction methods using spline functions

Habib Benali, Jeanpierre V. Guedon, Irene Buvat, Melanie Pelegrini, Yves J. Bizais, Robert Di Paola

Proceedings Volume 2299, Mathematical Methods in Medical Imaging III; (1994) https://doi.org/10.1117/12.179255
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

The conventional approach to tomographic reconstruction in the presence of noise consists in finding some compromise between the likelihood of the noisy projections and the expected smoothness of the solution, given the ill-posed nature of the reconstruction problem. Modelling noise properties is usually performed in iterative reconstruction schemes. In this paper, an analytical approach to the reconstruction from noisy projections is proposed. A statistical model is used to separate the relevant part of the projections from noise before the reconstruction. As reconstruction of sampled noise-free projections is still an ill- posed problem, a continuity assumption regarding the object to be reconstructed is also formulated. This assumption allows us to derive a spline filtered backprojection in order to invert the Radon operator. Preliminary results show the interest of combining continuity assumptions with noise modelling into an analytical reconstruction procedure.

Citation Download Citation

Habib Benali, Jeanpierre V. Guedon, Irene Buvat, Melanie Pelegrini, Yves J. Bizais, and Robert Di Paola "Statistical model for tomographic reconstruction methods using spline functions", Proc. SPIE 2299, Mathematical Methods in Medical Imaging III, (8 July 1994); https://doi.org/10.1117/12.179255

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available