Tensor Completion for Estimating Missing Values in Visual Data

Liu, Ji; Weiss, Tomer; Wonka, Peter; Ye, Jieping

doi:10.1109/tpami.2012.39

Cited by 1,731 publications

(1,594 citation statements)

References 33 publications

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“…To show the advantage of adding the robust error term E for support detection, we do a comparison with another low-rank texture completion method based on matrix completion [25]. In Figure 3, we first corrupted an input lowrank image with a ground truth support Ω, then we generate a new support Ω…”

Section: Solution Via Linearized Alternating Direction Methodsmentioning

confidence: 99%

“…We use Ω as the input support for our method and the LRTC method [25] and compare their completion results. In the comparison, we set parameters λ = 0.001, α = 0.85 for our algorithm and use DCT as the basis for B 1 and B 2 .…”

Section: Solution Via Linearized Alternating Direction Methodsmentioning

confidence: 99%

“…PΩ(A) = PΩ(D), which does not exploit the sparse prior at all). This is also the method which some of the latest texture completion methods such as LRTC [25] are based upon.…”

Section: Simulations and Experimentsmentioning

confidence: 99%

See 2 more Smart Citations

Repairing Sparse Low-Rank Texture

Liang

Ren

Zhang

et al. 2012

Lecture Notes in Computer Science

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Abstract. In this paper, we show how to harness both low-rank and sparse structures in regular or near regular textures for image completion. Our method leverages the new convex optimization for low-rank and sparse signal recovery and can automatically correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Through experimental comparisons with existing image completion systems (such as Photoshop) our method demonstrate significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.

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Section: Solution Via Linearized Alternating Direction Methodsmentioning

confidence: 99%

Section: Solution Via Linearized Alternating Direction Methodsmentioning

confidence: 99%

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Repairing Sparse Low-Rank Texture

Liang

Ren

Zhang

et al. 2012

Lecture Notes in Computer Science

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show abstract

“…Therefore, sparse representation [26,25,18] is generated accordingly, which calls for modeling data vectors as a linear combination of a few elements from an overcomplete dictionary. Depending on the sparse reconstruction coefficients, sparse representation has also been used for many matching and classification applications in computer vision domain, such as object tracking [24], object or face recognition [22], image inpainting [20]. In comparison with conventional sparse representation, where the bases in dictionary are selected manually or generated by a dictionary learning model, we propose a large scale dictionary selection model using low rank constraint, which can retain the original property of the data.…”

Section: Related Workmentioning

confidence: 99%

Abnormal event detection in crowded scenes using sparse representation

Cong

Yuan

Liu

2013

Pattern Recognition

Self Cite

288

192

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“…Nevertheless, since the rank of a multi-way array is discrete, rank minimization problems are usually hard to solve and sometimes NP hard. Then researchers usually replace rank in the objective function with nuclear norm [14]. It corresponds to the sum of singular values, which can be used as convex envelope of the rank function [15].…”

Section: Introductionmentioning

confidence: 99%

Low rank canonical polyadic decomposition of tensors based on group sparsity

Han¹,

Albera²,

Kachenoura³

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-A new and robust method for low rank Canonical Polyadic (CP) decomposition of tensors is introduced in this paper. The proposed method imposes the Group Sparsity of the coefficients of each Loading (GSL) matrix under orthonormal subspace. By this way, the low rank CP decomposition problem is solved without any knowledge of the true rank and without using any nuclear norm regularization term, which generally leads to computationally prohibitive iterative optimization for largescale data. Our GSL-CP technique can be then implemented using only an upper bound of the rank. It is compared in terms of performance with classical methods, which require to know exactly the rank of the tensor. Numerical simulated experiments with noisy tensors and results on fluorescence data show the advantages of the proposed GSL-CP method in comparison with classical algorithms.

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Tensor Completion for Estimating Missing Values in Visual Data

Cited by 1,731 publications

References 33 publications

Repairing Sparse Low-Rank Texture

Repairing Sparse Low-Rank Texture

Abnormal event detection in crowded scenes using sparse representation

Low rank canonical polyadic decomposition of tensors based on group sparsity

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