Fast and Accurate Tensor Completion With Total Variation Regularized Tensor Trains

Ko, Ching-Yun; Batselier, Kim; Daniel, Luca; Yu, Wenjian; Wong, Ngai

doi:10.1109/tip.2020.2995061

Cited by 48 publications

(18 citation statements)

References 32 publications

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“…(2) TMac [36]; (3) TMac-TT method [13]; (4) SiLRTC-TT method [13]; (5) PCLR method [37]; (6) TTC and TTC-TV method [28].…”

Section: Experiments and Results 41 Experimental Parameter Selectionmentioning

confidence: 99%

“…Another completion model, which combined TT rank with TV is proposed in ref. [28] by assuming tensor train structures in the underlying regression model. This model is rephrased as a regression task and uses the alternating linear scheme to update tensor train cores, but the result also shows that the alternating direction method of multipliers (ADMM)-TV method performs better than this method in relative standard error (RSE) and peak signal-tonoise ratio (PSNR) scores.…”

Section: Introductionmentioning

confidence: 99%

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Low tensor-train rank with total variation for magnetic resonance imaging reconstruction

Chen

Cao

2021

Sci. China Technol. Sci.

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The model by imposing the low-rank minimization has been proved to be effective for magnetic resonance imaging (MRI) completion. Recent studies have also shown that imposing tensor train (TT) and total variation (TV) constraint on tensor completion can produce impressive performance, and the lower TT-rank minimization constraint can be represented as the guarantee for global constraint, while the total variation as the guarantee for regional constraint. In our solution, a new approach is utilized to solve TT-TV model. In contrast with imposing the alternating linear scheme, nuclear norm regularization on TT-ranks is introduced in our method as it is an effective surrogate for rank optimization and our solution does not need to initialize and update tensor cores. By applying the alternating direction method of multipliers (ADMM), the optimization model is disassembled into some sub-problems, singular value thresholding can be used as the solution to the first sub-problem and soft thresholding can be used as the solution to the second sub-problem. The new optimization algorithm ensures the effectiveness of data recovery. In addition, a new method is introduced to reshape the MRI data to a higher-dimensional tensor, so as to enhance the performance of data completion. Furthermore, the method is compared with some other methods including tensor reconstruction methods and a matrix reconstruction method. It is concluded that the proposed method has a better recovery accuracy than others in MRI data according to the experiment results.

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“…(2) TMac [36]; (3) TMac-TT method [13]; (4) SiLRTC-TT method [13]; (5) PCLR method [37]; (6) TTC and TTC-TV method [28].…”

Section: Experiments and Results 41 Experimental Parameter Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low tensor-train rank with total variation for magnetic resonance imaging reconstruction

Chen

Cao

2021

Sci. China Technol. Sci.

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“…Though still lacking in sufficient theoretical foundations and algorithmic variety when compared to its matrix-based counterpart, tensor completion has already a quite rich literature [1], which includes (among other approaches) methods based on lowrank decomposition models. In addition to the classical Canonical Polyadic Decomposition (CPD) and/or Tucker decomposition [7,8,9,10], less well-known models, such as t-SVD [11], tensor trains [12] (and tensor rings [2]), and Mdecomposition [13], have been studied in the context of the completion problem. The model order (e.g., the tensor rank in CPD) is almost always assumed a-priori known.…”

Section: Introductionmentioning

confidence: 99%

Rank-Revealing Block-Term Decomposition for Tensor Completion

Rontogiannis

Giampouras

Kofidis

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous and diverse applications. In this paper, BTD is employed for the completion of a tensor from its partially observed entries. A novel method is proposed, which is based on the idea of imposing column sparsity jointly on the BTD factors and in a hierarchical manner. This way the number of block terms and their ranks can also be estimated, as the numbers of factor columns of non-negligible magnitude. Following a block successive upper bound minimization (BSUM) approach with appropriate choice of the surrogate majorizing functions is shown to result in an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which is fast converging and enjoys high computational efficiency, as it relies in its iterations on small-sized sub-problems with closed-form solutions. Simulation results with both synthetic and real data are reported, which demonstrate the effectiveness of the proposed scheme.

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“…Recently, research in tensor completion (TC), which is a higher-order extension of matrix completion, has achieved a consistent performance in a variety of real-world applications [15][16][17][18]. Given a tensor with incomplete entries, tensor completion methods such as recent low-rank based tensor completion (LRTC) [19] and simultaneous tensor decomposition and completion (STDC) [20] use low-rank factorization to model the available data entries, which are then used for completion to recover the missing values [21][22][23]. TC methods have already been used in electroencephalography (EEG) to recover missing samples, showing better performances than other simple imputation methods [24,25].…”

Section: Introductionmentioning

confidence: 99%

A hybrid method to select morphometric features using tensor completion and F-score rank for gifted children identification

Zhang

Feng

Han

et al. 2021

Sci. China Technol. Sci.

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Gifted children are able to learn in a more advanced way than others, probably due to neurophysiological differences in the communication efficiency in neural pathways. Topological features contribute to understanding the correlation between the brain structure and intelligence. Despite decades of neuroscience research using MRI, methods based on brain region connectivity patterns are limited by MRI artifacts, which therefore leads to revisiting MRI morphometric features, with the aim of using them to directly identify gifted children instead of using brain connectivity. However, the small, high-dimensional morphometric feature dataset with outliers makes the task of finding good classification models challenging. To this end, a hybrid method is proposed that combines tensor completion and feature selection methods to handle outliers and then select the discriminative features. The proposed method can achieve a classification accuracy of 93.1%, higher than other existing algorithms, which is thus suitable for the small MRI datasets with outliers in supervised classification scenarios.

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Fast and Accurate Tensor Completion With Total Variation Regularized Tensor Trains

Cited by 48 publications

References 32 publications

Low tensor-train rank with total variation for magnetic resonance imaging reconstruction

Low tensor-train rank with total variation for magnetic resonance imaging reconstruction

Rank-Revealing Block-Term Decomposition for Tensor Completion

A hybrid method to select morphometric features using tensor completion and F-score rank for gifted children identification

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