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In this paper, we propose a spatially adaptive denoising algorithm using local statistics for a single image corrupted by Gaussian noise. The proposed algorithm consists of two stages: noise detection and noise removal filtering. To corporate desirable properties into denoising process, local weighted mean, local weighted activity, and local maximum are defined. Using the local statistics, constraint for noise detection is defined. In addition, a modified Gaussian noise removal filter based on the local statistics is used to control the degree of noise suppression. The experimental results demonstrate the capability of the proposed algorithm.