Image Multiplicative Denoising Using Adaptive Euler’s Elastica as the Regularization

Variational models involving Euler’s elastica energy have been widely used in many fields of digital image processing, such as image inpainting and additive Gaussian noise removal. In this paper, according to the signal dependence of multiplicative noise, the Euler’s elastica functional is modified to adapt for the multiplicative denoising problem. And a novel multiplicative noise removal model based on adaptive Euler’s elastica is proposed. Furthermore, we develope two fast numerical algorithms to solve this high-order nonlinear model: Aiming at the evolution case of Euler–Lagrange equation, a semi-implicit iterative scheme is designed and the additive operator splitting algorithm is used to speed up the calculation; Expanding the augmented Lagrangian algorithm that has been successfully applied in recent years, we obtain a restricted proximal augmented Lagrangian method. Numerical experiments show the effectiveness of the two algorithms and the significant advantages of our model over the standard total variation denoising model in alleviating the staircase effect and restoring the tiny geometrical structures, especially, the line-like feature.