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

A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations
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Year:    2009

Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 4 : pp. 353–376

Abstract

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 function $\theta$. The 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2009.m9001s

Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 4 : pp. 353–376

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Algorithm of denoising image restoration total variation second-order functional.

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