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Estimating the noise parameter in magnitude magnetic resonance (MR) images is important in a wide range of applications. We propose an automatic noise estimation method that does not rely on a substantial proportion of voxels being from the background. Specifically, we model the magnitude of the observed signal as a mixture of Rice distributions with common noise parameter. The expectation-maximization (EM) algorithm is used to estimate all parameters, including the common noise parameter. The algorithm needs initializing values for which we provide some strategies that work well. The number of components in the mixture model also needs to be estimated en route to noise estimation and we provide a novel approach to doing so. Our methodology performs very well on a range of simulation experiments and physical phantom data. Finally, the methodology is demonstrated on four clinical datasets.