A neutrosophic filter for high-density Salt and Pepper noise based on pixel-wise adaptive smoothing parameter

• Neutrosophic indeterminacy of a pixel quantified by a Neutrosophic Set is applied to measure pixel similarity.
• Neutrosophic indeterminacy is used as an indicator of image contents.
• A pixel-wise adaptive function for smoothing parameter is designed.
• The proposed filter has excellent performances of noise removal and detail preservation.

Image indeterminacy has been neglected in most traditional filtering algorithms. This paper proposes a pixel-wise adaptive neutrosophic filter based on neutrosophic indeterminacy feature to remove high-level Salt-and-Pepper noise. In the proposed algorithm, the indeterminacy of a pixel is quantified by a Neutrosophic Set and innovatively exploited as an efficient characteristic of measuring the similarity of pixels. In order to adjust the smoothing parameter of the weight function pixel-wise adaptively, the uncertainty of a pixel is utilized as an indicator of image contents. Extensive experiments on numerous images demonstrate that with a 3 × 3 window, our method outperforms many existing denoising methods in terms of noise suppression and detail preservation.