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Abstract : |
We describe a method for removing noise from digital images, based on a statistical model of the coe#cients of an overcomplete multi-scale oriented basis. Neighborhoods of coe#cients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coe#cients in the neighborhood, and is thus able to account for the empirically observed correlation between the amplitudes of pyramid coe#cients. Under this model, the Bayesian least squares estimate of each coe#cient reduces to a weighted average of the local linear (Wiener) estimate over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive Gaussian noise of known covariance that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error. In addition, we demonstrate the performance of the algorithm in removing sensor noise from high-ISO digital camera images. The artifacts arising from many imaging devices are quite di#erent from the images that they contaminate, and this di#erence allows humans to "see past " the artifacts to the underlying image. The goal of image restoration is to relieve human observers from this task (and perhaps even to improve upon their abilities) by reconstructing a plausible estimate of the original image from the distorted or noisy observation. A prior probability model for both the noise and for uncorrupted images is of central importance for this application. # During the development of this work, VS was on leave from Drexel University, and was supported by an, |
