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 - <p style="text-align: justify;">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.</p>