(untitled) (Journal of Computational Mathematics, 2018)
Ultrasound imaging technique is one of the most non-invasive, practically harmless to the human body, accurate, cost effective and real-time techniques in medical diagnosis. However, ultrasound images suffer from the so-called speckle noise because of the imaging principle. The speckle noise reduces the quality and visibility of ultrasound images, thereby decreasing overall reliability of the images and interfering with the clinical diagnosis. In this paper, we propose a novel variational model under a combination of total variation regularization and Weberized total variation regularization and prove the existence and uniqueness of the minimizer for the variational problem. In order to efficiently solve the associated Euler-Lagrange equation consisting of nonlinear partial differential equation, we apply a finite difference method and develop several numerical techniques for solving the resulting discrete system. Numerical experiments on various synthetic and real ultrasound images not only confirm that our improved model is effective, but also it can provide significant improvement over evaluated models. Moreover, they also show that our proposed multigrid method has great potential applications to medical ultrasound imaging technique in delivering fast, accurate, and visually pleasing restoration results.