Direct Sparse Deblurring

We propose a deblurring algorithm that explicitly takes into account the sparse characteristics of natural images and does not entail solving a numerically ill-conditioned backward-diffusion. The key observation is that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. Following an “analysis-by-synthesis” approach, an explicit generative model is used to compute a sparse representation of the blurred image, and the coefficients of which are used to combine elements of the original basis to yield a restored image. We compare our algorithm against the state of the art in variational methods as well as wavelet-based algorithms.

• Type: Journal
• Year: 2011
• Where: JMIV
• Authors: Yifei Lou, Andrea L. Bertozzi, Stefano Soatto
• Keywords: Explicit Generative Model, Image, JMIV 2011, Sparse