A relaxation method for smooth tomographic reconstruction of binary axially symmetric objects

Maïtine Bergounioux (1) , Ali Srour (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper we study a minimization problem which appears in tomographic reconstruction. The problem is known to be ill posed. The object to reconstruct is assumed to be binary so that the intensity function belongs to {0,1}. Therefore the feasible set is not convex and its interior is empty for most usual topologies. We propose a relaxed formulation of the problem . We prove existence of solutions and give optimality conditions. In this paper we study a minimization problem which appears in tomographic reconstruction. The problem is known to be ill posed. The object to reconstruct is assumed to be binary so that the intensity function belongs to $\{0,1\}$. Therefore the feasible set is not convex and its interior is empty for most usual topologies. We propose a relaxed formulation of the problem . We prove existence of solutions and give optimality conditions.

Mots clés: Variational method; Relaxation; Lagrange multipliers; Mathematical programming

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Ali Srour. A relaxation method for smooth tomographic reconstruction of binary axially symmetric objects. Pacific journal of optimization, 2009, 5 (1), pp.39-51. ⟨hal-00259967⟩