Abstract: In order to separate different features of image,this paper presents a variational model for image decomposition.Meanwhile a new cartoon-texture dictionary learning algorithm is proposed.In the model,we introduce an incoherence promoting term,which encourages different components to be as independent as possible.Using decreasing gradient optimization algorithm,an alternate dictionary learning algorithm with constraint is presented.Numerical experiments show that the learned dictionaries by the proposed algorithm can describe the different components of image effectively,and lead to high quality image decomposition and denoising performance.