We propose a technique for image denoising by solving a nonconvex optimal control problem with the state and controller connected on a manifold described by a nonlinear elliptic equation. The existence of a control able to denoise an initial blurred image is proved and the optimality conditions are determined by a passing to the limit technique in an appropriate approximating problem, involving the Legendre-Fenchel relations. An algorithm constructed on the basis of the theoretical results is developed and numerical simulations are provided.