An Adaptive Image Decomposition Model Based On Fractional Derivatives

Image decomposition is a preprocessing process, which is widely used in various fields, especially in the field of image denoising and image inpainting. The image decomposition method decomposes the different components of the image into two parts: structure and texture.The structure of the image is the overall framework, including the main geometric features of the image information. The texture part is the detail information of the image, including the oscillation of the image or the noise information. The advantages and disadvantages of the image decomposition technology depend on the effect of the corresponding algorithm in the extraction of the noise, the important geometric features and the texture information of the image.Based on the study of the fractional derivative, an adaptive image decomposition model based on the fractional derivative is proposed which splits an image into its cartoon component and texture part. The cartoon component of an image is modeled by a fractional order total variation norm. The texture part is described by the L1 norm. The fractional derivative used in the new model and the coefficient to model texture are determined by the image itself, which reflects the adaptability of the new model. According to the criterion of energy reduction, the selection rules of different fractional derivatives are established. The alternating minimization method and split bregman algorithm are used to solve the new model. In order to test the validity of the new model, the new model is compared with the Meyer model. Experimental results show that the new model is better than Meyer model in image decomposition. The new model can better avoid the staircase effect. The new model is more effective in maintaining the image texture details and edge stability.The main work and innovations of this paper include the following aspects: first, this paper deeply studies the three definitions of the fractional derivative, and introduces the realization of the fractional derivative in matlab. Second, the classical total variation model and Split Bregman algorithm are introduced. Third, the adaptability of the fractional derivative order and the parameters describing the texture part in the model are discussed. Fourth, the fractional derivative is introduced into image decomposition, and an adaptive image decomposition model based on fractional derivative is proposed.