Image restoration using space-variant Gaussian scale mixtures in overcomplete pyramids

In recent years, Bayes least squares-Gaussian scale mixtures (BLS-GSM) has emerged as one of the most powerful methods for image restoration. Its strength relies on providing a simple and, yet, very effective local statistical description of oriented pyramid coefficient neighborhoods via a GSM vector. This can be viewed as a fine adaptation of the model to the signal variance at each scale, orientation, and spatial location. Here, we present an enhancement of the model by introducing a coarser adaptation level, where a larger neighborhood is used to estimate the local signal covariance within every subband. We formulate our model as a BLS estimator using space-variant GSM. The model can be also applied to image deconvolution, by first performing a global blur compensation, and then doing local adaptive denoising. We demonstrate through simulations that the proposed method, besides being model-based and noniterative, it is also robust and efficient. Its performance, measured visually and in L2-norm terms, is significantly higher than the original BLS-GSM method, both for denoising and deconvolution.