Image Decomposition of Partly Noisy Images

Abstract In this paper, we firstly propose a new variational model for partly noisy image decomposition by introducing a texture detecting function. Secondly, we prove the existence and uniqueness of minimal solutions of our proposed model. Thirdly, we give our algorithm, and write down the pseudo-codes of the specific steps. Finally, we show some numerical experiments, and the simulation results show that our model can effectively decompose cartoon and texture for images with Gaussian noise.