Abstract : Regularization is a common procedure when dealing with inverse problems. Because of the ill-posedness of many inverse problems, one needs to add some constraints as regularization to the problem in order to get a satisfactory solution. A difficulty when using multiple constraints is to properly choose a weighting parameter for each constraint. We propose here a vector field regularization method that combines in a single constraint the two well-known regularization methods namely Tikhonov regularization and smoothing regularization. The particularity of this new method is that one have only one balance parameter to determine. We also suggest a robust implementation of the proposed method based on the equivalent generalized diffusion equation in some particular cases. This implementation is illustrated on a set of vector fields of fluid motion
https://hal.inria.fr/inria-00360904
Contributor : Arthur Vidard
<>
Submitted on : Friday, February 13, 2009 - 9:10:19 AM
Last modification on : Wednesday, April 11, 2018 - 1:50:53 AM
Long-term archiving on: Saturday, November 26, 2016 - 5:28:18 AM
Innocent Souopgui, François-Xavier Le Dimet, Arthur Vidard. Vector field regularization by generalized diffusion. [Research Report] RR-6844, INRIA. 2009, pp.20. ⟨inria-00360904v2⟩
