Abstract
A novel partial differential equation (PDE)—based mixed image noise removal technique is proposed in this article. The considered approach filters successfully the images corrupted by combined Poisson–Gaussian noise by using a nonlinear fourth-order PDE-based denoising model that is proposed and carefully investigated here. Thus, a rigorous mathematical treatment of the validity of this model is performed, the existence of a weak solution of it being demonstrated. Then, the nonlinear PDE model is solved numerically by constructing a stable and fast-converging finite difference-based approximation scheme that is consistent to it. Mixed noise reduction experiments illustrating the effectiveness of the proposed approach are also discussed.
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Barbu, T. Mixed Noise Removal Framework Using a Nonlinear Fourth-Order PDE-Based Model. Appl Math Optim 84 (Suppl 2), 1865–1876 (2021). https://doi.org/10.1007/s00245-021-09813-4
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DOI: https://doi.org/10.1007/s00245-021-09813-4
Keywords
- Mixed Poisson–Gaussian noise removal
- Nonlinear PDE-based model
- Well-posedness
- Numerical approximation scheme
- Finite difference method