Total Variation Regularization Solved by Multi-grid Method and Applied in Image Denoising
多网格法解总变分问题及在医学图像增强中的应用

The isotropic diffusion method for image denoising such as those based on the Laplace regularization can smooth out the noise in image, but it may simultaneously blur the edge or boundary of the objects. In order to overcome this problem, recently many researchers pay attention to the smooth method based on the total variation (TV) regularization because it can reserve or even enhance the information of edge when smoothing the noise. However, since equation system deduced by TV method is a strongly nonlinear system, the convergence rate is very slow when solving TV equations using relaxation method. So in this paper, we introduce the multi-grid algorithm and conjugate gradient (CG) algorithm to solve this system. By smoothing out the noise in the echocardiograpgic images, numerical results indicate that the convergence rate of CG is fast, the algorithm of multi-grid has more efficiency and the image can be recovered with satisfied result even contamination of strong noise. As a result, the multi-grid algorithm is a good alternative method for solving the TV questions.