Deblurring-by-Denoising using Spatially Adaptive Gaussian Scale Mixtures in Overcomplete Pyramids

In a previous work, we presented an extension of the original Bayes least squares-Gaussian scale mixtures (BLS-GSM) denoising algorithm that also compensated the blur. However, that method had some problems: a) it could not compensate for some blurring kernels; b) its performance depended critically on having an accurate estimation of the original power spectral density (PSD); and c) it could not be easily adapted to a spatially variant description of the image statistics. In this work we propose a two-step restoration method that overcomes these problems by first performing a global blur image compensation, and then applying a spatially adaptive local denoising, in an overcomplete pyramid. Our method is efficient, robust and non-iterative. We demonstrate through simulations that it provides state-of-the-art performance.