Two-level adaptive denoising using Gaussian scale mixtures in overcomplete oriented pyramids

We describe an adaptive denoising method for images decomposed in overcomplete oriented pyramids. Our approach integrates two kinds of adaptation: 1) a ´coarse´ adaptation, where a large window is used within each subband to estimate the local signal covariance; 2) a ´fine´ adaptation, which uses small neighborhoods of coefficients modelled as the product of a Gaussian and a hidden multiplier, i.e., as Gaussian scale mixtures (GSM). The former provides adaptation to local spectral features, whereas the latter adapts to local energy fluctuations. We formulate our method as a Bayes least squares estimator using spatially variant GSMs. We also discuss the importance of image representation, compare the results using two different representations with complementary features, and study the effect of merging their results. We demonstrate through simulation that our method surpasses the state-of-the-art performance, in a L₂-norm sense.