Wavelet Frame Based Image Restoration with Missing/damaged Pixels

This paper addresses the problem of how to recover degraded images with partial image pixels being missing during transmission or damaged by impulsive noise. A wide range of image restoration tasks are covered in the mathematical model considered in this paper, e.g. image deblurring, image inpainting and super-resolution imaging. Based on the assumption that nature images are likely to have a sparse representation in wavelet tight frame domain, we propose a regularization based approach to recover degraded images by enforcing the analysis-based sparsity prior of images in tight frame domain. The resulting minimization problem can be efficiently solved by the split Bregman method ([28]). 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 and the robustness to mis-detection errors of missing/damaged pixels, and is compared favorably against existing algorithms.