Based Variational Partial Differential Equations Of Image Processing, And A Class Of Very Small Energy Functional Part,

Many approaches have been developed to process digital images, and it is difficult to say which one is more natural than the other. Partial differential equations (PDEs) and variational approaches is one of important methods. Traditionally applied in physics, these methods have been successfully and widely to image processing over last decades.In this paper, some methods are introduced, which process images based on PDEs and variational approaches, as well as analyzed. In particular, the ROF model of wide application and the Meyer model which is put forward recently are analyzed and compared. Some examples are given to show disadvantage and advantage of the two methods. The existence of the Meyer model is shown. The second part of the paper, it is shown the partial regularity of minimizer of energy functional, where integrand function satisfies linear growth. In the course of proof, we show the space exists. In the space, singular part of energy functional minimizer vanishes. Then by means of Holder estimates of quasi-elliptic equations which had existed, partial regularity of minimizer of functional is gained.