A lagrangian scheme for the solution of the optimal mass transfer problem

A lagrangian method to numerically solve the L^2 optimal mass transfer problem is presented. The initial and final density distributions are approximated by finite mass particles having a gaussian kernel. Mass conservation and the Hamilton-Jacobi equation for the potential are identically satisfied by constant mass transport along straight lines. The scheme is described in the context of existing methods to solve the problem and a set of numerical examples including applications to medical imagery are presented.

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