J Portilla, V Strela, M Wainwright, E P Simoncelli.
Image Denoising using Scale Mixtures of Gaussians in the Wavelet Domain.
IEEE Transactions on Image Processing. vol 12, no. 11, pp. 1338-1351, November 2003.
We have presented a denoising method based on a local Gaussian scale mixture model in an overcomplete oriented pyramid representation. Our statistical model differs from previous models in a number of important ways. First, many previous models have been based on either separable orthogonal wavelets, or redundant versions of such wavelets. In contrast, our model is based on an overcomplete tight frame that is free from aliasing, and that includes basis functions that are selective for oblique orientations. The increased redundancy of the representation and the higher ability to discriminate orientations results in improved performance. Second, our model explicitly incorporates the covariance between neighboring coefficients (for both signal and noise), as opposed to considering only marginal responses or local variance. Thus, the model captures correlations induced by the overcomplete representation as well as correlations inherent in the underlying image, and it can handle Gaussian noise of arbitrary power spectral density. Third, we have included a neighbor from the same orientation and spatial location at a coarser scale (a parent), as opposed to considering only spatial neighbors within each subband.