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Wavelet Based Restoration of Images with Missing or Damaged Pixels

Published online by Cambridge University Press:  28 May 2015

Hui Ji ,
Zuowei Shen  and
Yuhong Xu
Hui Ji*
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Zuowei Shen*
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Yuhong Xu*
Affiliation:
Temasek Laboratories, National University of Singapore, 2 Science Drive 2, Singapore 117543
*
Corresponding author. Email: matjh@nus.edu.sg
Corresponding author. Email: matzuows@nus.edu.sg
Corresponding author. Email: tslxyh@nus.edu.sg
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Abstract

This paper addresses the problem of how to restore degraded images where the pixels have been partly lost during transmission or damaged by impulsive noise. A wide range of image restoration tasks is covered in the mathematical model considered in this paper - e.g. image deblurring, image inpainting and super-resolution imaging. Based on the assumption that natural images are likely to have a sparse representation in a wavelet tight frame domain, we propose a regularization-based approach to recover degraded images, by enforcing the analysis-based sparsity prior of images in a tight frame domain. The resulting minimization problem can be solved efficiently by the split Bregman method. Numerical experiments on various image restoration tasks - simultaneously image deblurring and inpainting, super-resolution imaging and image deblurring under impulsive noise - demonstrated the effectiveness of our proposed algorithm. It proved robust to mis-detection errors of missing or damaged pixels, and compared favorably to existing algorithms.

Keywords

Image restorationimpulsive noisetight framesparse approximationsplit Bregman method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 2 , May 2011 , pp. 108 - 131
Copyright
Copyright © Global-Science Press 2011

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