Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train

By Johann A. Bengua, Ho N. Phien, Hoang Duong Tuan, Minh N. Do. IEEE Transactions on Image Processing, 2016

461 citations recorded by the source corpus.

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/514deb81fde464579b1853108d207f27efc90fa6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Shutao Li
2. Leyuan Fang
3. Renwei Dian

In Computational Mechanics

1. Shutao Li
2. Leyuan Fang
3. Renwei Dian
4. José M. Bioucas-Dias
5. Antonio J. Plaza
6. Marian-Daniel Iordache
7. Marcelo Pereyra
8. David J. Brady

In Computer Vision and Pattern Recognition

1. Leyuan Fang
2. Renwei Dian
3. Shutao Li
4. José M. Bioucas-Dias
5. Yu Liu
6. Xun Chen
7. Zengfu Wang
8. Jiayi Ma

Citations in the corpus

• Learning a Low Tensor-Train Rank Representation for Hyperspectral Image Super-Resolution (2019, methodology): “The low TT rank (LTTR) prior has been demonstrated to be very effective in the color image and videos completion [19] and outperforms the Tucker rank based methods.”
• Fusing Hyperspectral and Multispectral Images via Coupled Sparse Tensor Factorization (2018, methodology): “Recently, tensor-based methods have been successfully applied to multi-frame data restoration [31]– [34], recognition [35], [36], and unmixing [37], etc.”