  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.
