Parts for the Whole: The DCT Norm for Extreme Visual Recovery

TL;DR

This paper introduces a novel DCT norm for extreme visual recovery, effectively reconstructing images with over 90% missing pixels by leveraging global smoothness properties, outperforming existing methods.

Contribution

The paper proposes the DCT norm, a new regularization technique based on the Discrete Cosine Transform, to improve image recovery in highly incomplete data scenarios.

Findings

Outperforms state-of-the-art methods in PSNR and SSIM.

The DCT norm generalizes the TV norm, capturing global smoothness.

Effective for images with over 90% missing pixels.

Abstract

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.