Novel variational model for inpainting in the wavelet domain

Abstract: Wavelet domain inpainting refers to the process of recovering the missing coefficients during the image compression or transmission stage. Recently, an efficient algorithm framework which is called Bregmanized operator splitting (BOS) was proposed for solving the classical variational model of wavelet inpainting. However, it is still time-consuming to some extent due to the inner iteration. In this paper, a novel variational model is established to formulate this reconstruction problem from the view of image decomposition. Then an efficient iterative algorithm based on the split-Bregman method is adopted to calculate an optimal solution, and it is also proved to be convergent. Compared with the BOS algorithm the proposed algorithm avoids the inner iteration and hence is more simple. Numerical experiments demonstrate that the proposed method is very efficient and outperforms the current state-of-the-art methods, especially in the computational time.