Parts for the Whole: The DCT Norm for Extreme Visual Recovery
This addresses the problem of recovering highly incomplete images for applications in computer vision, representing an incremental advance over existing low-rank methods that fail beyond 90% missing values.
The paper tackles the extreme visual recovery problem where over 90% of pixel values are missing, proposing a DCT norm that exploits smoothness to achieve superior performance in terms of peak signal-to-noise ratio and structural similarity compared to state-of-the-art methods.
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.