Handling noise in image deconvolution with local/non-local priors

Non-blind deconvolution consists in recovering a sharp latent image from a blurred image with a known kernel. Deconvolved images usually contain unpleasant artifacts due to the ill-posedness of the problem even when the kernel is known. Making use of natural sparse priors has shown to reduce ringing artifacts but handling noise remains limited. On the other hand, non-local priors have shown to give the best results in image denoising. We propose in this paper to combine both local and non-local priors to handle noise. We show that the blur increases the self-similarity within an image and thus makes non-local priors a good choice for denoising blurred images. However, denoising introduces outliers which are not Gaussian and should be well modeled. Experiments show that our method produces a better image reconstruction both visually and empirically compared to methods some popular methods.