Image denoising using a local Gaussian scale mixture model in the wavelet domain
Vasily Strela, Javier Portilla, Eero P. Simoncelli · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
The statistics of photographic images, when decomposed in a multiscale wavelet basis, exhibit striking non-Gaussian behaviors. The joint densities of clusters of wavelet coefficients are well-described as a Gaussian scale mixture: a jointly Gaussian vector multiplied by a hidden scaling variable. We develop a maximum likelihood solution for estimating the hidden variable from an observation of the cluster of coefficients contaminated by additive Gaussian noise. The estimated hidden variable is then used to estimate the original noise-free coefficients. We demonstrate the power of this model through numerical simulations of image denoising.