Low-Rank tensor completion based on nonconvex regularization

Su, Xinhua; Ge, Huanmin; Liu, Zeting; Shen, Yanfei

doi:10.1016/j.sigpro.2023.109157

Cited by 9 publications

(2 citation statements)

References 39 publications

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“…SPCTV 4 : the smooth PARAFAC tensor completion and total variation method [23], which used the PD (PARAFAC decomposition, a derivation of Tucker decomposition) framework and constrained the TV on every factor matrix of PD respectively.…”

Section: Experimental Results and Analysesmentioning

confidence: 99%

“…It is a typical ill-posed inverse problem, generally solved by exploiting the image priors [1,2], such as smoothness, sparsity, and low rankness. In recent years, tensor analysis including tensor low-rank decomposition and tensor completion, has attracted increasing attention [3][4][5][6]. A color image itself is an order-3 tensor, or it can be used to construct a high order (greater than 3) tensor, then the image inpainting problem becomes a tensor completion problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme

Ma,

Fan,

Fang

et al. 2023

Preprint

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Employing low tensor rank decompositions in image inpainting has attracted increasing attention. This paper exploits a novel tensor-augmentation schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed augmentation schemes enhance the low-rankness of an image under three tensor decompositions: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solve the image inpainting problem with three low-rank con-strained models which use the matrix rank, TT rank, and tubal rank as constrained priors re-spectively. The tensor tubal rank and tensor train multi-rank are developed from t-SVD and TT decomposition respectively. We exploit efficient ADMM algorithms for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and supe-rior to numerous close methods.

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Section: Experimental Results and Analysesmentioning

confidence: 99%