  Here we study the extreme visual recovery problem, in which over 90\% of
pixel values in a given image are missing. Existing low rank-based algorithms
are only effective for recovering data with at most 90\% missing values. Thus,
we exploit visual data's smoothness property to help solve this challenging
extreme visual recovery problem. Based on the Discrete Cosine Transformation
(DCT), we propose a novel DCT norm that involves all pixels and produces smooth
estimations in any view. Our theoretical analysis shows that the total
variation (TV) norm, which only achieves local smoothness, is a special case of
the proposed DCT norm. We also develop a new visual recovery algorithm by
minimizing the DCT and nuclear norms to achieve a more visually pleasing
estimation. Experimental results on a benchmark image dataset demonstrate that
the proposed approach is superior to state-of-the-art methods in terms of peak
signal-to-noise ratio and structural similarity.
