Recently, many variational models using high order derivatives have been proposed to accomplish advanced tasks in image processing. Even though these models are effective in fulfilling those tasks, it is very challenging to minimize the associated high order functionals. In , we focused on a recently proposed mean curvature based image denoising model and developed an efficient algorithm to minimize it using augmented Lagrangian method, where minimizers of the original high order functional can be obtained by solving several low order functionals. Specifically, these low order functionals either have closed form solutions or can be solved using FFT. Since FFT yields exact solutions to the associated equations, in this work, we consider to use only approximations to replace these exact solutions in order to reduce the computational cost. We thus employ the Gauss-Seidel method to solve those equations and observe that the new strategy produces almost the same results as the previous one but needs less computational time, and the reduction of the computational time becomes salient for images of large sizes.