Image Variational Decomposition Based on Dual Method

In the paper, we firstly recommend a new variational model for image decomposition into cartoon and texture or noise by introducing a new function in Sobolev space, in order to overcome the inconsistency between the theoretical model and numerical simulation. Secondly, we prove the existence of minimal solutions of the improved ROF energy functional. Subsequently, we also introduce two additional improved models in the same way. Finally, we show some numerical experiments of our improved ROF models, and correspondingly compare them with those of the ROF model, VO model and TV1  H model. The results show that our models work well.