NONLOCAL SECOND-ORDER GEOMETRIC EQUATIONS ARISING IN TOMOGRAPHIC RECONSTRUCTION

Ali Srour (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines do not evolve along normal directions, and the nonlocal term is not of “convolution type”. On the other hand, the speed is not necessarily bounded compared to the nonlocal term. We prove a existence and uniqueness results of our model.

Mots clés: "Nonlocal Hamilton-Jacobi equations" "Tomographic reconstruction" "Nonlocal front propagation " "level-set approach" "Viscosity solutions".; Nonlocal Hamilton-Jacobi equations" "Tomographic reconstruction" "Nonlocal front propagation " "level-set approach" "Viscosity solutions

Domaines: Equations aux dérivées partielles [math.AP]

Ali Srour. NONLOCAL SECOND-ORDER GEOMETRIC EQUATIONS ARISING IN TOMOGRAPHIC RECONSTRUCTION. 2007. ⟨hal-00136314⟩