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<p>This article tackles the main issues related to image restoration, including the preservation of contours, removal of the staircasing effect, and reduction of mixture noise. For this purpose, we introduced a novel minimization problem, based on a PDE-constraint whose nonlinear structure relies on the solution itself. For the non-convex cost function, it contains a regularization term chosen by combining the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation> norms, and the fidelity term is the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm. First, we examine the theoretical characteristics of the suggested PDE-constrained approach and present certain well-posedness outcomes. In order to solve numerically the minimization problem, we utilized the infamous ADMM method. Finally, we validate the efficacy of the non-convex PDE-constrained model through extensive denoising experiments, encompassing diverse noisy images.</p>

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Identification of Gaussian and poisson noise through non-convex optimization with a non-local PDE constraint of r[u]-laplace type

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Ziad Zaabouli,
  • Lekbir Afraites,
  • Amine Laghrib,
  • Aissam Hadri

摘要

This article tackles the main issues related to image restoration, including the preservation of contours, removal of the staircasing effect, and reduction of mixture noise. For this purpose, we introduced a novel minimization problem, based on a PDE-constraint whose nonlinear structure relies on the solution itself. For the non-convex cost function, it contains a regularization term chosen by combining the \(L^p\) L p and \(L^q\) L q norms, and the fidelity term is the \(L^2\) L 2 -norm. First, we examine the theoretical characteristics of the suggested PDE-constrained approach and present certain well-posedness outcomes. In order to solve numerically the minimization problem, we utilized the infamous ADMM method. Finally, we validate the efficacy of the non-convex PDE-constrained model through extensive denoising experiments, encompassing diverse noisy images.