Fast Bayesian blind deconvolution with Huber Super Gaussian priors

• Published in: Digital signal processing Vol. 60; no. C
• Main Authors: Zhou, Xu, Vega, Miguel, Zhou, Fugen, Molina, Rafael, Katsaggelos, Aggelos K.
• Format: Journal Article
• Language: English
• Published: United States Elsevier 06.09.2016
• Subjects: blind deconvolution; image deblurring; image restoration; MATHEMATICS AND COMPUTING; variational Bayesian
• ISSN: 1051-2004

We report expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. In conclusion, extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.