In this paper, we propose a novel multiplanar autoregressive (AR) model toexploit the correlation in cross-dimensional planes of a similar patch groupcollected in an image, which has long been neglected by previous AR models. Onthat basis, we then present a joint multiplanar AR and low-rank based approach(MARLow) for image completion from random sampling, which exploits the nonlocalself-similarity within natural images more effectively. Specifically, themultiplanar AR model constraints the local stationarity in differentcross-sections of the patch group, while the low-rank minimization captures theintrinsic coherence of nonlocal patches. The proposed approach can be readilyextended to multichannel images (e.g. color images), by simultaneouslyconsidering the correlation in different channels. Experimental resultsdemonstrate that the proposed approach significantly outperformsstate-of-the-art methods, even if the pixel missing rate is as high as 90%.
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