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This paper proposes a novel approach to remove salt-and-pepper noise from a given noisy image. The proposed algorithm is based on statistical quantities such as mean and standard deviation. It determines the intensity to be placed on the impulse point by calculating the eligibility of the nearby points in a very simple way. This method works iteratively and removes all the impulse points restoring the edges and minute details. The proposed algorithm is very efficient and gives better results than various existing algorithms. The performance of the proposed method are compared with other existing methods with images of noise density as high as 99% and is found to perform better.