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arXiv · 2110.09298

"Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos

Chenjian Pan·Chen Ling·Hongjin He·Liqun Qi·Yanwei Xu
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Abstract

Recovering color images and videos from highly undersampled data is a fundamental and challenging task in face recognition and computer vision. By the multi-dimensional nature of color images and videos, in this paper, we propose a novel tensor completion approach, which is able to efficiently explore the sparsity of tensor data under the discrete cosine transform (DCT). Specifically, we introduce two ``sparse + low-rank'' tensor completion models as well as two implementable algorithms for finding their solutions. The first one is a DCT-based sparse plus weighted nuclear norm induced low-rank minimization model. The second one is a DCT-based sparse plus $p$-shrinking mapping induced low-rank optimization model. Moreover, we accordingly propose two implementable augmented Lagrangian-based algorithms for solving the underlying optimization models. A series of numerical experiments including color image inpainting and video data recovery demonstrate that our proposed approach performs better than many existing state-of-the-art tensor completion methods, especially for the case when the ratio of missing data is high.

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Chenjian Pan, Chen Ling, Hongjin He, Liqun Qi, Yanwei Xu. 2021-10-18. "Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos. https://arxiv.org/abs/2110.09298

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