Heat flows and related minimization problem in image restoration

A new anisotropic diffusion model is proposed for image restoration and segmentation, which is closely related to the minimization problems for the unconstrained total variation E(u) = ∫Ω α(x)βu + (β/2)u − I2. Existence, uniqueness, and stability of the viscosity solutions of the equation are proved. The experimental results are given and compared with the existing models in the framework of image restoration. The improvement on preserving sharp edges by using the new model is visible.