In this paper,we generalize the Ekeland variation principle to vector valued function and get Ekeland variation principle of vector valued function whose form is identical with Ekeland variation principle.

Image decomposition based on wavelet and variational functional;

Some constitutive equations of damage problems are discussed based on the general constitutive form of irreversible thermodynamic processes, and the corresponding damage variational functional, from which the FEM formualtion can be derived,is obtained from the augmented variational functional.

The zoomed image is found by minimizing the variational functional in the wavelet domain which uses the Besov norm to measure the regularity of the image.