Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain

J Portilla, V Strela, M J Wainwright and E P Simoncelli

Published in Proc 8th IEEE Int'l Conf on Image Proc (ICIP), vol.II pp. 37--40, Oct 2001.
© IEEE Computer Society

DOI: 10.1109/ICIP.2001.958418

  • Reprint (ps)
    • We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each coefficient of the pyramid is modeled as the product of two independent random variables: an element of a Gaussian random field, and a hidden multiplier with a marginal log-normal prior. The latter modulates the local variance of the coefficients. We assume subband coefficients are contaminated with additive Gaussian noise of known covariance, and compute a MAP estimate of each multiplier variable based on observation of a local neighborhood of coefficients. Conditioned on this multiplier, we then estimate the subband coefficients with a local Wiener estimator. Unlike previous approaches, we (a) empirically motivate our choice for the prior on the multiplier; (b) use the full covariance of signal and noise in the estimation; (c) include adjacent scales in the conditioning neighborhood. To our knowledge, the results are the best in the literature, both visually and in terms of squared error.

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