Wavelet Based Restoration of Images with Missing or Damaged Pixels
Hui Ji 1*, Zuowei Shen 1, Yuhong Xu 21 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543.
2 Temasek Laboratories, National University of Singapore, 2 Science Drive 2, Singapore 117543.
Received 2 March 2010; Accepted (in revised version) 24 June 2010
Available online 7 April 2011
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 -- \eg 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.
Key words: Image restoration, impulsive noise, tight frame, sparse approximation, split Bregman method.
Email: firstname.lastname@example.org (H. Ji), email@example.com (Z. Shen), firstname.lastname@example.org (Y. Xu)