Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling

Fuente: arXiv
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Autores principales: Li, Wei, Li, Yuyang, Du, Kaile, Yu, Yi, Liu, Guangcan
Formato: Preprint
Publicado: 2026
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author Li, Wei
Li, Yuyang
Du, Kaile
Yu, Yi
Liu, Guangcan
author_facet Li, Wei
Li, Yuyang
Du, Kaile
Yu, Yi
Liu, Guangcan
contents The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.
format Preprint
id arxiv_https___arxiv_org_abs_2604_17001
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
Li, Wei
Li, Yuyang
Du, Kaile
Yu, Yi
Liu, Guangcan
Computer Vision and Pattern Recognition
Artificial Intelligence
The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.
title Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
topic Computer Vision and Pattern Recognition
Artificial Intelligence
url https://arxiv.org/abs/2604.17001