A fractional-order derivative based variational framework for image denoising
Fangfang Dong, Yunmei Chen · Inverse Problems and Imaging · 2016
In this paper, we propose a unified variational framework for noiseremoval, which uses a combination of different orders of fractionalderivatives in the regularization term of the objective function.The principle of the combination is taking the order two or higherderivatives for smoothing the homogeneous regions, and a fractionalorder less than or equal to one to smooth the locations near theedges. We also introduce a novel edge detector to better detectedges and textures. A main advantage of this framework is thesuperiority in dealing with textures and repetitive structures aswell as eliminating the staircase effect. To effectively solve theproposed model, we extend the first-order primal dual algorithm tominimize a functional involving fractional-order derivatives. A setof experiments demonstrates that the proposed method is able toavoid the staircase effect and preserve accurately edges andstructural details of the image while removing the noise.