  In this paper, we propose a novel multiplanar autoregressive (AR) model to
exploit the correlation in cross-dimensional planes of a similar patch group
collected in an image, which has long been neglected by previous AR models. On
that basis, we then present a joint multiplanar AR and low-rank based approach
(MARLow) for image completion from random sampling, which exploits the nonlocal
self-similarity within natural images more effectively. Specifically, the
multiplanar AR model constraints the local stationarity in different
cross-sections of the patch group, while the low-rank minimization captures the
intrinsic coherence of nonlocal patches. The proposed approach can be readily
extended to multichannel images (e.g. color images), by simultaneously
considering the correlation in different channels. Experimental results
demonstrate that the proposed approach significantly outperforms
state-of-the-art methods, even if the pixel missing rate is as high as 90%.
