Image denoising via adjustment of wavelet coefficient magnitude correlation

We describe a novel method of removing additive white noise of known variance from photographic images. The method is based on a characterization of the statistical properties of natural images represented in a complex wavelet decomposition. Specifically, we decompose the noisy image into wavelet subbands, estimate the autocorrelation of both the noise-free raw coefficients and their magnitudes within each subband, impose these statistics by projecting onto the space of images having the desired autocorrelations, and reconstruct an image from the modified wavelet coefficients. This process is applied repeatedly, and can be accelerated to produce optimal results in only a few iterations. Denoising results compare favorably to three reference methods, both perceptually and in terms of mean squared error.