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.