Tensor Completion for Estimating Missing Values in Visual Data

By Ji Liu, Przemyslaw Musialski, Peter Wonka, Jieping Ye. 2009

2,089 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “In this respect, this situation is quite different from the growing area of tensor completion, see, e.g., [92,182], where the selection of the entries is usually prescribed by the application.”
Hyperspectral Image Super-Resolution via Non-local Sparse Tensor Factorization (2017, methodology): “In the past years, tensor factorization has been successfully applied into multiframe data denoising [10, 21], completion [41, 17, 40], compressive sensing [36] and classification [35].”
Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, methodology): “Recently, robust PCA (RPCA) methods have been emerged to solve the non-Gaussian noise model and computation issues associated with large-scale problems based on various optimization methods [8], [12], [16]–[18] and these optimization methods extended to the tensor-based methods [19], [20].”
A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion (2013, background): “Recently, [45] proposes tensor completion based on minimizing tensor n -rank, the matrix rank of mode-n matricization of a tensor.”
Sparse reconstruction cost for abnormal event detection (2011, methodology): “The key part of our algorithm is the sparsity pursuit , which has been a hot topic in machine learning recently and includes cardinality sparsity [11], group sparsity [28], matrix or tensor rank sparsity [17].”
Robust Low-Rank Tensor Recovery: Models and Algorithms (2013, methodology): “In the Singleton model, the tensor rank regularization term is the sum of the N nuclear norms This form of CTrank ( X ) was also considered in [32, 20, 46] for recovering low-rank tensors from partial observations of the data.”
Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm (2019, methodology): “…RIPT upon various scenes and noise, as they are complementary when Nevertheless, the singleton model [43] used in RIPT may lead to a suboptimal value, since the sum of nuclear norms (SNN) [44] is not the convex envelope of the corresponding sum of ranks [45]. with infrared small target detection.”
A Survey of Urban Reconstruction (2013, methodology): “Another method proposed by Liu et al. [LMWY09, LMWY13] aims at inpainting of missing image data.”
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery (2013, background): “For ease of stating results, suppose that Let T r denote the set of all such tensors.”
Less Is More: Towards Compact CNNs (2016, methodology): “In [31], the authors proposed to minimize the average rank of diﬀerent unfolding of a tensor matrix.”
Pruning and Quantization for Deep Neural Network Acceleration: A Survey (2021, background): “Sparse constraints [259] applied tensor low rank constraints [147] and group sparsity [54] achieving a 70% reduction of neurons with a 0.”
Tensor Factorization for Low-Rank Tensor Completion (2018, methodology): “Recent research [2], [3], [6], [7], [10]–[13] shows that high dimensional tensor data of interest, such as videos and image collections, are usually intrinsically low-rank or approximately so.”
Multitask learning meets tensor factorization: task imputation via convex optimization (2014, background): “The overlapped trace norm (see [12, 15, 18, 22]) is defined as the sum of the trace norms of the mode-k unfoldings as follows:”
A Three-Operator Splitting Scheme and its Optimization Applications (2015, background): “5 We are grateful of Professor Ji Liu for sharing his data in [33] with us.”
A Bayesian tensor decomposition approach for spatiotemporal traffic data imputation (2019, methodology): “In the numerical experiment, we compare the BGCP model with two other tensor decomposition-based imputation methods: • high accuracy low-rank tensor completion (HaLRTC) (Liu et al., 2013), which is used in Ran et al. (2016), and • SVD-combined tensor decomposition (STD) (Chen et al., 2018).”
TensoRF: Tensorial Radiance Fields (2022, methodology): “In general, low-rank regularization is crucial in addressing many reconstruction problems, like matrix completion [1], compressive sensing [2], denoising [4]; tensor decomposition has also been widely used in tensor completion [5, 3], which is similar to our task.”
A Survey of Deep Learning-Based Object Detection (2019, background): “structure detection, researches propose strong baseline in both 2D images [192] [193] and 3D point clouds [194] [195] [196][197][198][199][200][201][202][203][204][205].”