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Volume 9, Issue 4
Efficient Homotopy Solution and a Convex Combination of ROF and LLT Models for Image Restoration

F. Yang, K. Chen & B. Yu

Int. J. Numer. Anal. Mod., 9 (2012), pp. 907-927.

Published online: 2012-09

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  • Abstract

The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm.

  • Keywords

Image restoration, total variation, fourth-order PDE, fixed point method, homotopy method, convex combination.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-907, author = {F. Yang, K. Chen and B. Yu}, title = {Efficient Homotopy Solution and a Convex Combination of ROF and LLT Models for Image Restoration}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {907--927}, abstract = {

The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/665.html} }
TY - JOUR T1 - Efficient Homotopy Solution and a Convex Combination of ROF and LLT Models for Image Restoration AU - F. Yang, K. Chen & B. Yu JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 907 EP - 927 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/665.html KW - Image restoration, total variation, fourth-order PDE, fixed point method, homotopy method, convex combination. AB -

The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm.

F. Yang, K. Chen and B. Yu. (2012). Efficient Homotopy Solution and a Convex Combination of ROF and LLT Models for Image Restoration. International Journal of Numerical Analysis and Modeling. 9 (4). 907-927. doi:
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