Nonlocal Second-Order Geometric Equations Arising in Tomographic Reconstruction

2007/03/13 by Ali Srour, Srour, Ali
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering

paper · doi:10.48550/arxiv.math/0703364

Abstract

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.

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

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