Considering that the variation methods for image multiplicative noise removal exhibit the staircase effect problem

we analyze the characteristic and correlation of several classical multiplicative denoising variation models. With the frequency characteristic of the fractional differential considered

a fractional-order convex variation model for multiplicative Gamma noise removal is proposed. Our fractional-order convex variation model is the fractional-order generalization of the classical I-divergence variation model. Based on duality theory

a fractional-order primal-dual algorithm to solve the model is proposed. The range of the parameter is given according to saddle-point theory to guarantee algorithm convergence. In terms of frequency domain aspects

the experiments verify that the proposed fractional-order variation model is effective in relaxing the staircase effect and preserving medium-frequency texture information in a cardiac ultrasound image

as well as high-frequency building edges information in the “Cameraman” image compared with the classical first-order variation model. The proposed fractional-order primal-dual algorithm can also effectively converge and exhibits a fast convergence speed. To produce denoised images with minimal loss of image details

this study proposes a fractional-order variation model for image multiplicative noise removal. Classical variation numerical algorithms need to compute the derivative of a non-differentiable function (i.e.

the fractional-order regulation term)

so we refer to a primal-dual algorithm based on a resolvent for an alternative solution. Experiment results indicate that the proposed model can effectively improve the image visual effect

and the adoptive numerical algorithm demonstrates a fast convergence speed.