Nonlocal Second-Order Geometric Equations Arising in Tomographic Reconstruction

Details Nonlocal Second-Order Geometric Equations Arising in Tomographic Reconstruction Nonlocal Second-Order Geometric Equations Arising in Tomographic Reconstruction

2007-03-13

arxiv.org/abs/math/0703364v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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.

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