On Optimal sparse control formulation for reconstruction of noise-affected images - Kohut, Peter (Modeling, Control and Information Technologies: Proceedings of International scientific and practical conference, 2025)
We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L^1 -control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic features of the considered parabolic problem is that the variable exponent p(t, x) and the diffusion anisotropic tensor D(t,x) are not well predefined a priori, but instead these characteristics non-locally depend on the form of the solution of this problem, i.e., p_u = p(t, x, u) and D_u = D (t, x, u). We prove the existence of optimal pairs with sparse L^1 -controls using for that the indirect approach and a special family of approximation problems.