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We introduce a simple spatially adaptive statistical model for wavelet image coefficients and apply it to image denoising. Our model is inspired by a recent wavelet image compression algorithm, the estimation-quantization (EQ) coder. We model wavelet image coefficients as zero-mean Gaussian random variables with high local correlation. We assume a marginal prior distribution on wavelet coefficients variances and estimate them using an approximate maximum a posteriori probability rule. Then we apply an approximate minimum mean squared error estimation procedure to restore the noisy wavelet image coefficients. Despite the simplicity of our method, both in its concept and implementation, our denoising results are among the best reported in the literature.