Alternating Direction Method for Image Inpainting in Wavelet Domain

Image inpainting in wavelet domain refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature and they produce high-quality reconstructed images. In this paper, we consider an unconstrained TV-regularized, l2-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of ADM for solving wavelet domain image inpainting problems. Numerical comparison results of ADM with some recent algorithms are also reported.