# Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion

arXiv: https://arxiv.org/abs/2305.07976 · HTML: https://mlsanity.com/paper/2305.07976/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 62 references that are in the map.
- First posted on arXiv 13 May 2023.

## Builds on (most cited first, 10 of 10)

- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Low-rank tensor completion: a Riemannian manifold preconditioning approach](https://mlsanity.com/paper/1605.08257/) (2016)
- [Riemannian Hamiltonian methods for min-max optimization on manifolds](https://mlsanity.com/paper/2204.11418/) (2022)
- [Alternating proximal gradient method for sparse nonnegative Tucker decomposition](https://mlsanity.com/paper/1302.2559/) (2013)
- [Effects of Spectral Normalization in Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2212.05331/) (2022)
- [Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid](https://mlsanity.com/paper/1909.09771/) (2019)
- [Efficient FPGA Implementation of Conjugate Gradient Methods for Laplacian System using HLS](https://mlsanity.com/paper/1803.03797/) (2018)

## Built on by (most cited first, 1 of 1)

- [Image Reconstruction using Superpixel Clustering and Tensor Completion](https://mlsanity.com/paper/2305.09564/) (2023)

## Abstract (arXiv)

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of such tensors. The factorization decouples the nonnegative constraints from the low-rank constraints. The resulting problem is an optimization problem on manifolds, and we propose a variant of Riemannian conjugate gradients to solve it. We test the proposed algorithm across various tasks such as colour image inpainting, video completion, and hyperspectral image completion. Experimental results show that the proposed method outperforms many state-of-the-art tensor completion algorithms.