This paper proposes a novel variational model and a fast algorithm for its numerical approximation to remove multiplicative noise from digital images.

By applying a maximum a posteriori (MAP), we obtained a strictly convex objective functional whose minimization leads to non-linear PDEs.

To this end, we develop an efficient non-linear multi-grid algorithm with an improved smoother and also discuss a local Fourier analysis of the associated smoothers which leads to a new and more effective smoother.

Experimental results using both synthetic and realistic images, illustrate advantages of our proposed model in visual improvement as well as an increase in the PSNR over comparing to related recent corresponding PDE methods.

We compare numerical results of new multi-grid algorithm via modified smoother with traditional time marching schemes and with multi-grid method via (local and global) fixed point smoother as well.