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.