Image restoration by mixture modelling of an overcomplete linear representation

We present a new image restoration method based on modelling the coefficients of an overcomplete wavelet response to natural images with a mixture of two Gaussian distributions, having non-zero and zero mean respectively, and reflecting the assumption that this response is close to be sparse. Including the observation model, the resulting procedure iterates between image reconstruction from the hard-thresholding of the response to the current estimate and a fast blur compensation step. Results indicate that our method compares favorably with current wavelet-based restoration methods.