Multiplicative Noise Removal And Its Fast Algorithm Based On High-order Variational Model

Image denoising problem can be divided into additive noise removal and multiplicative noise removal.The research of additive noise is more extensive.Later,with the popularity of multiplicative noise in images,the research on multiplicative noise becomes more and more in-depth.With the popularity of variational methods in additive noise,many variational models have also been proposed to solve multiplicative noise problems.The aforementioned works have studied the removal of multiplicative noise in terms of first order methods.But restoring images by first order model has many disadvantages.In the case of TV,it may cause the loss of contrast and staircase effect.The other first-order models also have the phenomenon that the edges and the corners are not good.In this paper,we propose a new method to remove the multiplicative noise in an image,in which the Total Generalized Variation(TGV)model and Total Curvature(TC)model.The split Bregman algorithm is used for the TGV variational model and the augmented Lagrangian algorithm is used for the TC variational model.Because the high-order model is complicated and has a long computation time,the numerical method based on Fast Fourier Transform(FFT)is used in this paper to speed up the computation.By comparing the TGV model,the TC model with the first-order Total Variation(TV)model and the second-order Hessian matrix,we conclude that: From the qualitative aspect,the high order TGV and TC model can remove the staircase effect,and can better keep the edge,corner and contrast of the image.The peak signal to noise ratio(PSNR)and the signal to noise ratio(SNR)of the high order model are higher from the quantitative aspect.Both the TGV model and the TC model can quickly reach the convergence state after denoising.Which verifies the effectiveness of high-order model in removing multiplicative noise.