# Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling

arXiv: https://arxiv.org/abs/2604.17001 · HTML: https://mlsanity.com/paper/2604.17001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Builds on (most cited first, 13 of 13)

- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Super SloMo: High Quality Estimation of Multiple Intermediate Frames for Video Interpolation](https://mlsanity.com/paper/1712.00080/) (2017)
- [Real-Time Intermediate Flow Estimation for Video Frame Interpolation](https://mlsanity.com/paper/2011.06294/) (2020)
- [Quadratic video interpolation](https://mlsanity.com/paper/1911.00627/) (2019)
- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Extracting Motion and Appearance via Inter-Frame Attention for Efficient Video Frame Interpolation](https://mlsanity.com/paper/2303.00440/) (2023)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Low-Rank Matrix and Tensor Completion via Adaptive Sampling](https://mlsanity.com/paper/1304.4672/) (2013)
- [Generalized Nonconvex Nonsmooth Low-Rank Minimization](https://mlsanity.com/paper/1404.7306/) (2014)
- [Recovery of Future Data via Convolution Nuclear Norm Minimization](https://mlsanity.com/paper/1909.03889/) (2019)
- [Time Series Forecasting via Learning Convolutionally Low-Rank Models](https://mlsanity.com/paper/2104.11510/) (2021)

## Abstract (arXiv)

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of textittensor 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.