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Optimal Sparse Control Formulation for Reconstruction of Noise-Affected Images
Version 1
: Received: 25 August 2023 / Approved: 28 August 2023 / Online: 29 August 2023 (03:18:06 CEST)
A peer-reviewed article of this Preprint also exists.
Kogut, P.; Kohut, Y. Optimal Sparse Control Formulation for Reconstruction of Noise-Affected Images. Axioms 2023, 12, 1073. Kogut, P.; Kohut, Y. Optimal Sparse Control Formulation for Reconstruction of Noise-Affected Images. Axioms 2023, 12, 1073.
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 L1-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 feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.
Keywords
optimal control; parabolic equation; variable order of nonlinearity; noncoercive problem; compensated compactness technique
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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