Table of Contents
International Journal of Computational Mathematics
Volume 2015, Article ID 860263, 17 pages
Research Article

A New Study of Blind Deconvolution with Implicit Incorporation of Nonnegativity Constraints

1Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, Liverpool L69 L7L, UK
2Department of Eye and Vision Science, University of Liverpool, Liverpool L69 3GA, UK

Received 1 July 2014; Revised 29 December 2014; Accepted 12 January 2015

Academic Editor: David Defour

Copyright © 2015 Ke Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The inverse problem of image restoration to remove noise and blur in an observed image was extensively studied in the last two decades. For the case of a known blurring kernel (or a known blurring type such as out of focus or Gaussian blur), many effective models and efficient solvers exist. However when the underlying blur is unknown, there have been fewer developments for modelling the so-called blind deblurring since the early works of You and Kaveh (1996) and Chan and Wong (1998). A major challenge is how to impose the extra constraints to ensure quality of restoration. This paper proposes a new transform based method to impose the positivity constraints automatically and then two numerical solution algorithms. Test results demonstrate the effectiveness and robustness of the proposed method in restoring blurred images.