(untitled) (Моделювання, керування та інформаційні технології, 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.