We study a forward-backward parabolic equation from the Perona-Malik model for image processing. Although this model and its numerical implementation have played some important role for edge enhancement and image restoration in image processing, the model itself has also raised many interesting and open mathematical problems. For example, the existence of solutions to the Perona-Malik equation with arbitrarily given initial data has remained unknown for many years until it was proved for one-dimensional problem a few years ago. In this talk, I will discuss a new approach of studying the n-dimensional Perona-Malik equation as a differential inclusion and report the recent result on the existence of infinitely many weak solutions to the Neumann boundary problem for Perona-Malik equation with arbitrary smooth non-constant initial data.