Image decolorization has a wide range of applications in digital printing, photo rendering and single-channel image processing. During the process of image decolorization, it is significant to retain more contrast infor-mation and avoid increasing the noise level of the original image. As we know, noise was hardly considered in previous decolorization methods. In this paper, we propose a new multi-tasking variational model with two tasks: decolorizing and denoising. The first task is image decolorization, that is, to transform color images to grayscale images. The other task is to control the noise level, and even eliminate the noise. Inspired by TV-Stokes model, we introduce the unit normal vector containing the basic geometry information of the color image in the model. The existence and the uniqueness of the solution to the varia-tional problems are proved. For the variational model, two numerical methods are adopted. At first, we use gradient descent method to obtain evolution equations and construct finite difference schemes to solve the corresponding equations of proposed variational model. Furthermore, an efficient augmented Lagrangian approach is applied to solve the multi-tasking variational model directly. For noisy images and clean images, we employ two output patterns of grayscale images respectively. Especially, our model is stable for the noisy images. Numerical results and comparisons show that the proposed model can produce highly competitive results in terms of decolorization quality of noisy images, edge preservation and adjustment of parameters.
