Image denoising by a nonlinear control technique

ABSTRACT 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.

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