We note that by doing this we are using the regularities of PDEs indirectly, because the comparison principle in PDE literature relies on the regularities through a regularization procedure.
The proposed methods are compared with several existing regularization methods through simulations.
Finally we obtained the regularization solution through solving the inverse problem.
Moreover, the regularization effect through the convexification of non-convex potential is embedded to represent fine scale behavior.
The de-noising process is performed using a multiplicative regularization method through an adaptive window whose shapes, sizes and orientations vary with the image structure.
The applicability of the approximate expressions is discussed by defining the problem of finding optimal regularization parameters through minimizing the expected true error.
For both models, we fit the regularization parameters through cross-validation and compared the mean squared error on a common held-out set of 16 arrays selected by removing one array from each node with replicates.
Inverse analysis is operated separately at each variable in the joint distribution model through regularization because of noise-contaminated measured responses.
Land reform tends to promote land redistribution through regularization of smallholder land invasions of large-scale landholdings, and by redistribution of public lands to smallholders in existing colonization frontiers.
If an arriving target training instance is incorrectly predicted then the ensemble is updated through the optimization procedure which aims to classify the next new example correctly without deviating too much from the original ensemble through regularization terms.
