Vector field regularization by generalized diffusion
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
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