This correspondence describes an iterative method for removing signal-independent, additive noise from digital images. The underlying concept of this fully automated method is noise filtering by use of local statistics. Assuming that the noise is statistically stationary, noise variance is estimated from an input image by utilizing its smallest local variances. Noise filtering is performed iteratively and terminates when the estimated noise variance converges to zero. The method successfully processes degraded images by filtering noise from regions of uniform intensity while preserving texture pixels and edges.