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Noise elimination plays a very important role in every aspect of image processing. De-noising is essential in order to enhance, analyze and interpret the important information in an image. Noise reduction should be performed on an image in a way that no important edge information in the image is lost. The Cross Sigma Filter and Recursive Cross Sigma Filter, two methods for de-noising an image, have been proposed in this paper. The proposed filters smooth an image while retaining important edge information. These suggested methods are compared with the other contemporary techniques and the results of the comparison establish the superiority of the proposed methods, both in terms of computational complexity and functional performance.