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With widely availed clinically used radionuclides, Cerenkov luminescence imaging (CLI) has become a potential tool in the field of optical molecular imaging. However, the impulse noises introduced by high-energy gamma rays that are generated during the decay of radionuclide reduce the image quality significantly, which affects the accuracy of quantitative analysis, as well as the three-dimensional reconstruction. In this work, a novel denoising framework based on fuzzy clustering and curvature-driven diffusion (CDD) is proposed to remove this kind of impulse noises. To improve the accuracy, the Fuzzy Local Information C-Means algorithm, where spatial information is evolved, is used. We evaluate the performance of the proposed framework systematically with a series of experiments, and the corresponding results demonstrate a better denoising effect than those from the commonly used median filter method. We hope this work may provide a useful data pre-processing tool for CLI and its following studies.