Anisotropic Diffusion with Nonlinear Structure Tensor

A new coupled diffusion is proposed for joint image restoration and discontinuity detection. The system consists of two types of diffusion, an anisotropic diffusion on an image for restoration and an isotropic diffusion on the structure tensor of the image for singularity extraction. The diffusion on the image is guided by the structure tensor, and the diffusion of the structure tensor is supervised by the image. The coupled system keeps the advantages of the anisotropic model given by Weickert for image restoration, while it performs better in orientation discontinuities than the linear structure tensor. The existence and uniqueness of the solution of the model are proved, and a convergent iteration scheme is given to solve the system. Numerical experiments both on synthetic and natural images are presented to demonstrate the performance of the model.

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