A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise, multiplicative noise destroys almost all information of the original image, especially for texture images. Motivated by the TV-Stokes model, we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper. In the first step, we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing. Once the isophote directions are constructed, an image is restored to fit the constructed directions in the second step. The existence and uniqueness of the solution to the variational problems are proved. In these two steps, we use the gradient descent method and construct finite difference schemes to solve the problems. Especially, the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation. Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.