Variational total curvature model for multiplicative noise removal

Abstract

The multiplicative noise removal problem has received considerable attention recently. To solve this problem, various variational models have been proposed, which minimise an energy functional composed of the data term and the regularisation term. Regarding the regularisation term, a first‐order model is frequently used to remove multiplicative noise, which may cause staircase effect and loss of contrast in the output image. In this study, the authors use a second‐order model, the total curvature (TC), to solve the above problem. The TC model has the benefit of removing the staircase effect and maintaining image edges, contrasts and corners. The augmented Lagrange method is utilised to solve the proposed TC model by introducing auxiliary variables, Lagrange multipliers and using alternating optimisation strategy. In each loop of optimisation, the fast Fourier transform, generalised soft threshold formulas, projection method and gradient descent method are integrated effectively. The experimental results show that the TC model can effectively remove staircase effect and preserve smoothness, via comparison with the first‐order model (total variation regularisation and Perona–Malik regularisation). Furthermore, the TC model is better than another second‐order model based on bounded Hessian regularisation in preserving contrast and corner.

Keywords

• variational total curvature model
• multiplicative noise removal problem
• first-order model
• second-order model
• TC model
• augmented Lagrange method