At present, most of image decomposition models only apply to some ideal images, such as, noise-free, without blurring and super resolution images, and so on. In this paper, they propose a novel decomposition model based on dual method and texture detecting function for noisy image. Firstly, they prove the existence of minimal solutions of the noisy decomposition model functional. Secondly, they write down an alterative implementation algorithm. Finally, they give some numerical experiments, which show that their model can effectively work for Gaussian noisy image decomposition.