Year: 2024
Type: article
Abstract: 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 thesecharacteristics 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.
Author: Peter Kohut
Institution: Oles Honchar Dnipro National University
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405275604