## A compound algorithm of denoising using second-order and fourth-order partial differential equations.(English)Zbl 1212.68383

Summary: We propose a compound algorithm for image restoration. The algorithm is a convex combination of the ROF model and the LET model with a parameter function $$\theta$$. Numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in $$L_2$$ norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.

### MSC:

 68U10 Computing methodologies for image processing 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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