Numerical approach for a relaxed minimization problem arising in tomographic reconstruction

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.

Keywords

• Tomographic reconstruction
• variational method
• relaxation
• Lagrange multipliers
• mathematical programming
• Lagrangian method