Sharpening is a key technology of infrared image enhancement, but the image’s noise will be enhanced because of the sharpening, and the signal-to-noise ratio will decrease. The algorithm is researched to sharpen the image without increasing the noise. The distribution difference between random noise and the real edge is analyzed, and the definitions of the membership and the probability relaxation are advanced to distinguish the illumination changes caused by real edges or noise in the infrared image. An algorithm based on the two methods are introduced. Different from the tranditional algorithms, this algorithm considers the spatial difference between the real edge and the noise. So this algorithm not only enhances the details, but also reduces the enhancement of random noise. As it is shown in experiments, the edge of the image is sharpened and the noise is suppressed. This algorithm has practicality and potential application value in the field of infrared images contrast enhancement.