We discuss the existence of solutions to an optimal control problem for Neumann boundary value Perona-Malik equations. The variable \begin{document}$ v $\end{document} is taken as a distributed control. minimize discrepancy between given distribution id="M6">\begin{document}$ u_d\in L^2(\Omega) and curren...

Abstract We discuss some optimal control problem for the evolutionary Perona–Malik equations with Neumann boundary condition. The variable v is taken as a distributed control. to minimize discrepancy between given distribution $$u_d\in L^2(\Omega )$$ u d ∈</mml:m...

We prove here an existence result for solutions for a parabolic equation, with non local coefficients arising in image processing. An image is a bounded function u : D → R defined on a rectangular region D. If the function u is not regular, the image is noisy and it is not possible to use it directly in applications, but is necessary to smooth it by means of a nonlinear evolution problem, with ...

Based on the renowned additive operator splitting (AOS) schemes that ensure equal treatment of all coordinate axis, accelerated AOS schemes for solving regularized Perona-Malik (P-M) equation are presented. These ameliorated AOS schemes are stable unconditionally, consistent with nonlinear parabolic equations under certain circumstance and demonstrate a remarkably economical CPU time. The paper...

In this paper, an image denoising operator de ned by a non-linear partial di erential equation(PDE) is presented. Similar to the operators proposed by Perona, Malik and Catt e et al., it can remove noise, enhance step-like edges and keep the locality of the edges. Its extra ability is to keep thin edges. The criterion for stopping time is also investigated. The new operator is capable of removi...

We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in an open set Ω ⊆ R, with Neumann boundary conditions. It is well known that in the one-dimensional case this problem does not admit any global C solution if the initial condition u0 is transcritical, namely when |∇u0(x)| − 1 is a sign changing function in Ω. In this paper we show that this result cannot be ...

We investigate how the Perona-Malik scheme evolves piecewise smooth initial data in one dimension. By scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size, we obtain a meaningful continuum limit. The resulting evolution can be seen as the gradient flow for an energy, just as the discrete evolutions are gradient flows for discrete energies. I...