Abstract
In this paper, we are interested in the mathematical and simulation study of a new non-convex constrained PDE to remove the mixture of Gaussian–impulse noise densities. The model incorporates a non-convex data-fidelity term with a fractional constrained PDE. In addition, we adopt a non-smooth primal-dual algorithm to resolve the obtained proximal linearized minimization problem. The non-convex fidelity term is used to handle the high-frequency of the impulse noise component, while the fractional operator enables the efficient denoising of smooth areas, avoiding also the staircasing effect that appears on the relevant variational denoising models. Moreover, the proposed primal-dual algorithm helps in preserving fine structures and texture with good convergence rate. Numerical experiments, including ultrasound images, show that the proposed non-convex constrained PDE produces better denoising results compared to the state-of-the-art denoising models.
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The authors are grateful to the anonymous reviewers for their insightful remarks and corrections. Their feedback had a remarkable insight on the new version.
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Hadri, A., Afraites, L., Laghrib, A. et al. A novel image denoising approach based on a non-convex constrained PDE: application to ultrasound images. SIViP 15, 1057–1064 (2021). https://doi.org/10.1007/s11760-020-01831-z
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DOI: https://doi.org/10.1007/s11760-020-01831-z