An Improved Variational Model and Its Numerical Solutions for Speckle Noise Removal from Real Ultrasound Images (Journal of Computational Mathematics, 2018)
Ultrasound imaging technique is one of the most non-invasive, practically harmless tothe 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 imagingprinciple. The speckle noise reduces the quality and visibility of ultrasound images, therebydecreasing overall reliability of the images and interfering with the clinical diagnosis. Inthis paper, we propose a novel variational model under a combination of total variationregularization and Weberized total variation regularization and prove the existence anduniqueness of the minimizer for the variational problem. In order to efficiently solve theassociated Euler-Lagrange equation consisting of nonlinear partial differential equation, weapply a finite difference method and develop several numerical techniques for solving theresulting discrete system. Numerical experiments on various synthetic and real ultrasoundimages not only confirm that our improved model is effective, but also it can provide significantimprovement over evaluated models. Moreover, they also show that our proposedmultigrid method has great potential applications to medical ultrasound imaging techniquein delivering fast, accurate, and visually pleasing restoration results.