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1 results

  • Wavelet Based Restoration of Images with Missing or Damaged Pixels

  • Hui Ji, Zuowei Shen, Yuhong Xu
  • Journal:
    East Asian Journal on Applied Mathematics / Volume 1 / Issue 2 / May 2011
    Published online by Cambridge University Press:
    28 May 2015, pp. 108-131
    Print publication:
    May 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 - 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.