Fractional-order Variational Regularization for Image Decomposition

We propose new models for image decomposition which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a fractional variational formulation, the role of which is to better handle the texture details of image. We compute this decomposition by minimizing a convex functional which depends on the two variable u and v, alternatively in each variable. The resulting evolution equations are the gradient descent flow that minimizes the overall functional. The proposed models have been applied to real images with promising results; unlike the existing TV-based image restoration models, the proposed models don't suffer from block artifacts, staircase edges and false edge near the edges.