Image denoising using a scale mixture of Gaussians in the wavelet domain-英文文献.pdf

1338 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 12, NO. 11, NOVEMBER 2003 Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain Javier Portilla, Vasily Strela, Martin J. Wainwright, and Eero P. Simoncelli Abstract—We describe a method for removing noise from digital basic assumptions are commonly made in order to reduce di- images, based on a statistical model of the coefficients of an over- mensionality. The first is that the probability structure may be complete multiscale oriented basis. Neighborhoods of coefficients defined locally. Typically, one makes a Markov assumption, that at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden the probability density of a pixel, when conditioned on a set positive scalar multiplier. The latter modulates the local variance of of neighbors, is independent of the pixels beyond the neigh- the coefficients in the neighborhood, and is thus able to account for borhood. The second is an assumption of spatial homogeneity: the empirically observed correlation between the coefficient am- the distribution of values in a neighborhood is the same for all plitudes. Under this model, the Bayesian least squares estimate of such neighborhoods, regardless of absolute spatial position. The each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. Markov random field model that results from these two assump- We demonstrate through simulations with images contaminated by tions is commonly simplified by assuming the distributions are additive white Gaussian nois