Abstract：Based on the compressed sensing and sparse representation theory, and on the parallel
coordinate descent an image inpainting model method is proposed, which uses the method of wavelet
transform for image sparse representation, with sparse as the regularization term, and at the same time,
realizes global optimization based on the threshold of relaxation to mark function. The global optimal
solution can be obtained by using PCD. The proposed algorithm is verified from the peak signal to
noise ratio of convergence speed and visual effect. The results show that the new model has better
effect in both objective and subjective, and at the same time has faster convergence speed.
