Images, captured with digital imaging devices, often contain noise. In literature, many algorithms exist for the removal of white uncorrelated noise, but they usually fail when applied to images with correlated noise. In this paper, we design a new denoising method for the removal of correlated noise, by modeling the significance of the noise-free wavelet coefficients in a local window using a new significance measure that defines the “signal of interest” and that is applicable to correlated noise. We combine the intrascale model with a Hidden Markov Tree model to capture the interscale dependencies between the wavelet coefficients. We propose a denoising method based on the combined model and a less redundant wavelet transform. We present results that show that the new method performs as well as the state-of-the-art wavelet-based methods, while having a lower computational complexity.