A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter functionθ. The numerical experiments demonstrate that our compound al- gorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in L2 norm between the exact images and cor- responding 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 cor- responding 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.

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