We propose a nonlinear variational approach to remove impulsive noise in scalar images. Taking benefit from recent studies on the use of stochastic resonance and the constructive role of noise in nonlinear processes, our process is based on the classical restoration process of Perona-Malik in which a Gaussian noise is purposely injected. We show that this new process can outperform the original restoration process of Perona-Malik from which it is inspired.