Fast Bayesian blind deconvolution with Huber Super Gaussian priors

Xu Zhou*, Miguel Vega, Fugen Zhou, Rafael Molina, Aggelos K. Katsaggelos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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. Extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.

Original languageEnglish (US)
Pages (from-to)122-133
Number of pages12
JournalDigital Signal Processing: A Review Journal
Volume60
DOIs
StatePublished - Jan 1 2017

Keywords

  • Blind deconvolution
  • Image deblurring
  • Image restoration
  • Variational Bayesian

ASJC Scopus subject areas

  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics

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