A novel exponential tension field for salt-and-pepper image denoising

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.