Abstract:

We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each subband of the pyramid is modeled as the pointwise product of two independent random fields: a Gaussian Markov random field, and a hidden multiplier with a marginal log-normal prior. The latter thus modulates the local variance of the coefficients. We assume additive Gaussian noise of known covariance, and compute a MAP estimate of each multiplier variable based on observation of a local neighborhood of coefficients. Then, conditioned on this multiplier, we estimate the subband coefficients with a local Wiener estimator. Unlike previous models, we 1) motivate empirically our choice for the prior on the multiplier; 2) use the full covariance of signal and noise in the estimation; 3) include adjacent scales in the conditioning neighborhood. To our knowledge, the results are the best in the literature, both visually and in terms of MSE. We extend our ideas to the case of semiregular meshes and present the results of our surface denoising algorithm.