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Wavelet Based Restoration of Images with Missing or Damaged Pixels

Wavelet Based Restoration of Images with Missing or Damaged Pixels
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Year:    2011

East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 2 : pp. 108–131

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.020310.240610a

East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 2 : pp. 108–131

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Image restoration impulsive noise tight frame sparse approximation split Bregman method.

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