Tensor Completion through Total Variationwith Initialization from Weighted HOSVD

2020/03/20 by Zehan Chao, Chao, Zehan, Longxiu Huang +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2003.09062

openalex publication_date 2020/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD result as an initialization for the total variation. We have proved the accuracy of the weighted HOSVD algorithm from theoretical and numerical perspectives. In the numerical simulation parts, we also showed that by using the proposed initialization, the total variation algorithm can efficiently fill the missing data for images and videos.

Citations

• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition

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