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This paper presents a new concept of removing impulse noise through primary implicant elimination (PIE) applied to a logical system representation of the data. Applicable to binary and grayscale images, errors are corrected efficiently, in terms of the number of computations and memory requirements, while the fine details of the image are mostly preserved. Three filtering algorithms are presented: a general form in addition to iterative and switching variations. Experimental results on salt-and-pepper impulse noise, as well as on random-valued impulse noise, are compared against the performance of traditional median-based filters (both regular and switching) and are shown to be most successful in the often difficult case of when the original image contains many detailed patterns.