  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.
