| 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. |
