Abstract Image denoising is a very important problem in image processing field. In order to improve denoising effects and meanwhile keep image structures, a novel weighted total variation (WTV) model is proposed in this paper. The WTV model consists of data fidelity and norm based regularisation terms. In the WTV model, a weight function in exponential form is incorporated into the regularisation term, which only depends on the given image itself without extra parameters. The nonlinearly monotone formulation of helps to increase gaps between lower and higher frequencies of images, which is effective to highlight edges and keep textures. For solving the proposed model, the alternating direction method of multipliers is explored and the according convergence is analysed. Compared experiments of TV, HOTV, ATV and models are conducted and the results show the effectiveness and efficiency of the proposed model.

The images used in various practices are often disturbed by noise, such as Gaussian noise, speckled noise, and salt and pepper noise. Images with noise are one of the challenges for segmentation, since the noise may cause inaccurate segmented results. To cope with the effect of noise on images during segmentation, a novel active contour model is proposed in this paper. The newly proposed model consists of fitting term, regularization term and penalty term. The fitting term is designed using a Gaussian kernel function and fractional order differentiation with an adaptively defined fractional order, which applies different orders to different pixels. The regularization term is applied to maintain the smoothness of curves. In order to ensure stable evolution of curves, a penalty term is added into the proposed model. Comparison experiments are conducted to show the effectiveness and efficiency of the proposed model.