Split-Bregman iteration for framelet based image inpainting

Image inpainting plays a significant role in image processing and has many applications. Framelet based inpainting methods were introduced recently by Cai et al. (2007, 2009) [6,7,9] under an assumption that images can be sparsely approximated in the framelet domain. By analyzing these methods, we present a framelet based inpainting model in which the cost functional is the weighted ℓ1 norm of the framelet coefficients of the underlying image. The split-Bregman iteration is exploited to derive an iterative algorithm for the model. The resulting algorithm assimilates advantages while avoiding limitations of the framelet based inpainting approaches in Cai et al. (2007, 2009) [6,7,9]. The convergence analysis of the proposed algorithm is presented. Our numerical experiments show that the algorithm proposed here performs favorably.