Electron. J. Diff. Equ., Vol. 2013 (2013), No. 133, pp. 1-11.

Numerical approach for a relaxed minimization problem arising in tomographic reconstruction

Ali Srour, Mouhammad Jradeh

Abstract:
The purpose of this article is to develop a numerical scheme for a system of optimality conditions for a smooth minimization problem that arises in tomographic reconstruction of binary axially symmetric objects. The density function of the object with the Lagrange multipliers is seen as a saddle point of an associated Lagrangian, then we use the Usawa scheme mixed with descent gradient method to give the corresponding numerical scheme.

Submitted April 28, 2012. Published May 29, 2013.
Math Subject Classifications: 65K05, 65K15, 65K10.
Key Words: Tomographic reconstruction; variational method; relaxation; Lagrange multipliers; mathematical programming; Lagrangian method.

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Ali Srour
Department of Mathematics, Lebanese University
Hawch Al-Oumara, Zahleh, Lebanon
email: ali.srour.lb@gmail.com
Mouhammad Jradeh
Department of Mathematics, Lebanese University
Hawch Al-Oumara, Zahleh, Lebanon
email: mouhamad.jradeh@gmail.com

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