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We present a simple and fast algorithm for image noise estimation. The input image is assumed to be corrupted by additive zero mean Gaussian noise. To exclude structures or details from contributing to the noise variance estimation, a simple edge detection algorithm using first-order gradients is applied first. Then a Laplacian operator followed by an averaging over the whole image will provide very accurate noise variance estimation. There is only one parameter which is self-determined and adaptive to the image contents. Simulation results show that the proposed algorithm performs well for different types of images over a large range of noise variances. Performance comparisons against other approaches are also provided.