In this paper we propose a variational model for image restoration based on the minimization of a convex functional with a gradient constraint. This approach has a smoothing effect on the degraded image, as it does not allow rapid changes in the image content. We also consider the evolutionary model of the resulting nonlinear differential equation. Furthermore, we discuss the dual problem associated with the model and propose a numerical algorithm for approximating its solution.
Oana Carja. "A gradient constraint variational approach to image reconstruction." Differential Integral Equations 22 (3/4) 285 - 301, March/April 2009. https://doi.org/10.57262/die/1356019775