Image inpainting via singular value thresholding

Yeganli, S. Faegheh; Yu, Runyi

doi:10.1109/siu.2013.6531291

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…This completion problem has been applied in the famous Netflix problem [6], image inpainting problem [7] and machine learning [8,9]. In general, however, the problem (AMRM) is a challenging non-convex optimization problem and is known as NP-hard [10] due to the combinational nature of the rank function.…”

Section: Introductionmentioning

confidence: 99%

Exact recovery low-rank matrix via transformed affine matrix rank minimization

Cui

Peng

2018

Neurocomputing

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The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function is studied to approximate the rank of a matrix and translate this NP-hard problem into a transformed affine matrix rank minimization problem. The equivalence between these two problems is established, and we proved that the uniqueness of the global minimizer of transformed affine matrix rank minimization problem also solves affine matrix rank minimization problem if some conditions are satisfied. Moreover, we also proved that the optimal solution to the transformed affine matrix rank minimization problem can be approximately obtained by solving its regularization problem for some proper smaller λ > 0. Lastly, the DC algorithm is utilized to solve the regularization transformed affine matrix rank minimization problem and the numerical experiments on image inpainting problems show that our method performs effectively in recovering low-rank images compared with some stateof-art algorithms.

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Section: Introductionmentioning

confidence: 99%

Exact recovery low-rank matrix via transformed affine matrix rank minimization

Cui

Peng

2018

Neurocomputing

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“…The affine matrix rank minimization (AMRM) problem consisting of recovering a low-rank matrix that satisfies a given system of linear equality constraints is an important problem in recent years, and has attracted much attention in many applications such as machine learning [1], collaborative filtering in recommender systems [2,3], computer vision [4], network localization [5], system identification [6,7], control theory [8,9], and so on. A special case of AMRM is the matrix completion (MC) problem [10], it has been applied in the famous Netflix problem [11] and image inpainting problem [12]. Unfortunately, the problem AMRM is generally NP-hard [13] and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function.…”

Section: Introductionmentioning

confidence: 99%

Generalized singular value thresholding operator to affine matrix rank minimization problem

Cui¹,

Li²,

Peng³

et al. 2017

Preprint

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It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function. In this paper, a generalized singular value thresholding operator is generated to solve the affine matrix rank minimization problem. Numerical experiments show that our algorithm performs effectively in finding a low-rank matrix compared with some state-of-art methods.

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An Iterative Method for Tensor Inpainting Based on Higher-Order Singular Value Decomposition

Yeganli

Demirel

2017

Circuits Syst Signal Process

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Image inpainting via singular value thresholding

Cited by 3 publications

References 12 publications

Exact recovery low-rank matrix via transformed affine matrix rank minimization

Exact recovery low-rank matrix via transformed affine matrix rank minimization

Generalized singular value thresholding operator to affine matrix rank minimization problem

An Iterative Method for Tensor Inpainting Based on Higher-Order Singular Value Decomposition

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