A modified multi-grid algorithm for a novel variational model to remove multiplicative noise

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 partial differential equations. As a result, developing a fast numerical scheme is difficult because of the high nonlinearity and stiffness of the associated Euler-Lagrange equation and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient non-linear multi-grid algorithm with an improved smoother. We 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 peak signal-to-noise ratio over comparing to related recent corresponding PDE methods. We compare numerical results of new multigrid algorithm via modified smoother with traditional time marching schemes and with multigrid method via (local and global) fixed point smoother as well.