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

Abstract

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 1 Total variation is abbreviated to TV. The combination of an l 1 data fidelity and an l 2 penalty term is abbreviated to ( l 1 + l 2). The combination of an l 2 data fidelity and TV penalty term is abbreviated to ( l 2 + TV). The combination of an l 1 data fidelity and TV penalty term is abbreviated to ( l 1 + TV). The combination of an l 2 data fidelity and an l 2 penalty term is abbreviated to ( l 2 + l 2). 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.