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Title: Wavelet based restoration of images with missing or damaged pixels
Authors: Ji, H. 
Shen, Z. 
Xu, Y. 
Keywords: Image restoration
Impulsive noise
Sparse approximation
Split bregman method
Tight frame
Issue Date: May-2011
Citation: Ji, H., Shen, Z., Xu, Y. (2011-05). Wavelet based restoration of images with missing or damaged pixels. East Asian Journal on Applied Mathematics 1 (2) : 108-131. ScholarBank@NUS Repository.
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. © 2011 Global-Science Press.
Source Title: East Asian Journal on Applied Mathematics
ISSN: 20797362
DOI: 10.4208/eajam.020310.240610a
Appears in Collections:Staff Publications

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