Wavelet Based Restoration of Images with Missing or Damaged Pixels

作者：Ji Hui^*; Shen Zuowei; Xu Yuhong

来源：East Asian Journal on Applied Mathematics, 2011, 1(2): 108-131.

DOI：10.4208/eajam.020310.240610a

• Image restoration
• impulsive noise
• tight frame
• sparse approximation
• split Bregman method

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,Thy 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.

• 出版日期2011-5