Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation
Preprint Series # 778
Giga, Yoshikazu and Kuroda, Hirotoshi and Yamazaki, Noriaki Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation. (2006);
We consider a gradient flow system of total variation with constraint.
Our system is often used in the color image processing to remove a
noise from picture. In particular, we want to preserve the sharp edges of picture
and color chromaticity. Therefore, the values of solutions to our model is
constrained in some fixed compact Riemannian manifold. By this reason, it is
very difficult to analyze such a problem, mathematically. The main object of
this paper is to show the global solvability of a constrained singular diffusion
equation associated with total variation. In fact, by using abstract convergence
theory of convex functions, we shall prove the existence of solutions to
our models with piecewise constant initial and boundary data.