Fractional partial differential equation denoising models for texture image

In this paper, a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach are proposed to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image. By extending Green, Gauss, Stokes and Euler-Lagrange formulas to fractional field, we can find that the integer formulas are just their special case of fractional ones. In order to improve the denoising capability, we proposed 4 fractional partial differential equation based multi-scale denoising models, and then discussed their stabilities and convergence rate. Theoretic deduction and experimental evaluation demonstrate the stability and astringency of fractional steepest descent approach, and fractional nonlinearly multi-scale denoising capability and best value of parameters are discussed also. The experiments results prove that the ability for preserving high-frequency edge and complex texture information of the proposed denoising models are obviously superior to traditional integral based algorithms, especially for texture detail rich images.