EURASIP Journal on Applied Signal Processing 
Volume 2003 (2003), Issue 12, Pages 1167-1180
doi:10.1155/S1110865703308066

Spatially Adaptive Intensity Bounds for Image Restoration

Kaaren L. May,1 Tania Stathaki,2 and Aggelos K. Katsaggelos3

 1Snell and Wilcox Ltd., Liss Research Centre, Liss Mill, Mill Road, Liss, Hampshire, GU33 7BD, UK
2Communications and Signal Processing Group, Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2BT, UK
3Department of Electrical and Computer Engineering, Northwestern University, Evanston 60208-3118, IL, USA
Received 9 December 2002; Revised 24 June 2003

Abstract

Spatially-adaptive intensity bounds on the image estimate are shown to be an effective means of regularising the ill-posed image restoration problem. For blind restoration, the local intensity constraints also help to further define the solution, thereby reducing the number of multiple solutions and local minima. The bounds are defined in terms of the local statistics of the image estimate and a control parameter which determines the scale of the bounds. Guidelines for choosing this parameter are developed in the context of classical (nonblind) image restoration. The intensity bounds are applied by means of the gradient projection method, and conditions for convergence are derived when the bounds are refined using the current image estimate. Based on this method, a new alternating constrained minimisation approach is proposed for blind image restoration. On the basis of the experimental results provided, it is found that local intensity bounds offer a simple, flexible method of constraining both the nonblind and blind restoration problems.