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We describe a method for removing mixed noise from digital images which are contaminated by salt and pepper noise and Gaussian noise, based on cellular automata and Gaussian scale mixture. First we learn some rules by training on the salt and pepper noise images. These rules can then be used on the mixed noise images and remove the salt and pepper noise by CA filtering, after this, we decompose the image into subbands using the steerable pyramid, and then model the neighborhoods of coefficients using the Gaussian scale mixture: the product of a Gaussian random vector and an independent hidden random scalar multiplier. With this model, Bayesian least squares estimator is used to remove the residual noise. Denoising by this method can preserve the edges and details better than others.