Journal · 2026
A novel exponential tension field for salt-and-pepper image denoising
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- Citations
Abstract
Salt-and-pepper noise is a particularly challenging image degradation model because it corrupts pixels sparsely but severely, often disrupting edges, textures, and fine structural details. This paper presents the exponential tension field (ETF) as a geometrically grounded method for removing impulse noise.
ETF is formulated from an exponential gradient-based functional and implemented as a nonlinear, gradient-dependent diffusion operator that promotes smoothing in corrupted homogeneous regions while limiting diffusion across significant intensity transitions. The proposed method is discretized at the pixel level using a conservative finite-volume scheme and evaluated on standard grayscale benchmark images degraded by salt-and-pepper noise at various levels. We assess performance using PSNR, SSIM, precision, recall, F-measure, VIF, FOM, and MAE, along with runtime analysis and statistical testing. ETF is compared to representative classical, variational, and transform-based denoisers. Benchmark results show that ETF excels at restoring images, particularly under high-noise
conditions, while preserving edges and fine image structures. The method does not require training, is computationally efficient, and has a clear variational interpretation. The findings suggest that ETF is a viable and comprehensible geometry-based method for denoising salt-and-pepper images in the examined context, prompting further investigation into similar nonlinear diffusion operators for impulse-noise image restoration.
Keywords
Salt-and-pepper noiseImage denoisingExponential tension fieldNonlinear diffusionGeometric image processingEdge-preserving restoration
Other publications from the same authors
2027
Publication details
- Venue
- Scientific Reports
- Type
- Journal · 2026
- DOI
- 10.1038/s41598-026-58595-8
- Citations
- 0 · via Crossref, 1 November 2026
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APA
Torbaghan, S. M. K., Jajarmi, A., Moghaddam, Y. J., Torbaghan, S. F. K., & Torbaghan, S. F. K. (2026). A novel exponential tension field for salt-and-pepper image denoising. Scientific Reports. https://doi.org/10.1038/s41598-026-58595-8
Harvard
Torbaghan, S.M.K., Jajarmi, A., Moghaddam, Y.J., Torbaghan, S.F.K. and Torbaghan, S.F.K. (2026) 'A novel exponential tension field for salt-and-pepper image denoising', Scientific Reports. doi: 10.1038/s41598-026-58595-8.
IEEE
S. M. K. Torbaghan, A. Jajarmi, Y. J. Moghaddam, S. F. K. Torbaghan, and S. F. K. Torbaghan, "A novel exponential tension field for salt-and-pepper image denoising," Scientific Reports, 2026. doi: 10.1038/s41598-026-58595-8.
Vancouver
Torbaghan SMK, Jajarmi A, Moghaddam YJ, Torbaghan SFK, Torbaghan SFK. A novel exponential tension field for salt-and-pepper image denoising. Scientific Reports. 2026. doi: 10.1038/s41598-026-58595-8.
MLA
Torbaghan, Seyed Mehdi Kazemi, et al.. "A novel exponential tension field for salt-and-pepper image denoising." Scientific Reports, 2026. https://doi.org/10.1038/s41598-026-58595-8.
Chicago
Torbaghan, S. M. K., Jajarmi, A., Moghaddam, Y. J., Torbaghan, S. F. K., Torbaghan, S. F. K.. "A novel exponential tension field for salt-and-pepper image denoising." Scientific Reports (2026). https://doi.org/10.1038/s41598-026-58595-8.
BibTeX
@article{torbaghan2026, title={A novel exponential tension field for salt-and-pepper image denoising}, author={Torbaghan, Seyed Mehdi Kazemi and Jajarmi, Amin and Moghaddam, Yaser Jouybari and Torbaghan, Seyed Farhad Kazemian and Torbaghan, Seyed Farhad Kazemian}, journal={Scientific Reports}, year={2026}, doi={10.1038/s41598-026-58595-8}, }
