Reconstruction of a velocity field for a 3-D advection-diffusion equation

This work deals with the reconstruction of a piecewise constant velocity field for a 3-D advection-diffusion equation. Reconstructing a velocity field often plays an important role in understanding the formation and evolution of orogenic topography. In order to suppress measurement errors and to identify sharp features, we propose a new regularization integrating an l(1) data fidelity with a total variation(1) penalty term to reconstruct a piecewise constant velocity field. For testing the performance of our proposed regularization method, we compare four different regularization methods. From numerical experiments, we can draw conclusions: (I) an l(1) data fidelity can suppress measurement errors including Gaussian noise and non-Gaussian noise; (II) a total variation penalty term has the ability to identify sharp features. (C) 2011 Elsevier Masson SAS. All rights reserved.