A new learning Space-Variant anisotropic constrained-PDE for image denoising

• Published in: Applied mathematical modelling 2024-01, Vol.125, p.139-163
• Main Authors: Hadri, Aissam, Laghrib, Amine, El Mourabit, Idriss
• Format: Article
• Language: English
• Subjects: ADMM; Image denoising; Learning parameters; Spatial PDE; Tensor diffusion
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2023.09.022

In this paper, we propose an improved enhancement space-variant anisotropic PDE-constrained for image denoising, based on a learning optimization procedure. Since the tensor structure of the Weickert-type operators encodes three critical parameters: λ1,λ2 and θ, which define the local direction geometry in the image and also controls smoothing intensity along image features. We have then adopted an automatic estimation of these parameters based on a PDE-constrained optimization with a learning step of the additional information about the clean image. For the numerical solution of the computed free-noise image, we introduce a non-smooth Alternating Direction Method of Multipliers (ADMM) algorithm. The numerous tests in the experiments part incense, visually and quantitatively, the incomes of this new spatial tensor for PDE smoothing over the other denoising approaches. •An improved enhancement space-variant anisotropic PDE-constrained for image denoising is introduced.•An automatic estimation of the diffusion-tensor parameters based on a bilevel optimization with a learning step is involved.•A non-smooth ADMM algorithm is also performed to compute the solution of the optimization-constrained problem.•The comparative results demonstrates the performance of the proposed algorithm against complex noise structures.