Image inpainting with a wavelet domain Hidden Markov tree model

We present a novel technique for image inpainting, the problem of filling-in missing image parts. Image inpainting is ill-posed and we adopt a probabilistic model-based approach to regularize it. The main elements of our image model are, first, an over-complete complex-wavelet image representation, which ensures good shift invariance and directional selectivity and, second, a discrete-state/continuous-observation hidden Markov tree model for the wavelet coefficients, which captures key statistical properties of natural image wavelet responses, such as heavy-tailed histograms and persistence of large wavelet coefficients across scales. We show how these ideas can be integrated into a multi-scale generative process for natural images and present alternative deterministic and Markov chain Monte Carlo algorithms for image inpainting under this model. We demonstrate the effectiveness of the method in digitally restoring images of ancient wall-paintings.