A combination model for image denoising

作者：Xu, Yi-ping^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2016, 32(3): 781-792.

DOI：10.1007/s10255-016-0604-7

• image denoising
• partial differential equations
• split Bregman method
• algebraic multi-grid method
• Krylov subspace acceleration

In this paper, we propose an efficient combination model of the second-order ROF model and a simple fourth-order partial differential equation (PDE) for image denoising. The split Bregman method is used to convert the nonlinear combination model into a linear system in the outer iteration, and an algebraic multigrid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to analyze the parameter selection criteria and discuss the performance of the fourth-order PDE in the combination model. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.

• 出版日期2016-7
• 单位西南科技大学