Symmetry analysis for a fourth-order noise-reduction partial differential equation

We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary differential equations are reduced to second-order ordinary differential equations which are maximally symmetric. Finally, nonstatic closed-form solutions are also determined.