Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision
Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gu, Shuhang [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2016 |
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| Übergeordnetes Werk: |
Enthalten in: International journal of computer vision - Springer US, 1987, 121(2016), 2 vom: 18. Juli, Seite 183-208 |
|---|---|
| Übergeordnetes Werk: |
volume:121 ; year:2016 ; number:2 ; day:18 ; month:07 ; pages:183-208 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11263-016-0930-5 |
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OLC2057750760 |
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| 520 | |a Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. | ||
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| 700 | 1 | |a Feng, Xiangchu |4 aut | |
| 700 | 1 | |a Zhang, Lei |4 aut | |
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10.1007/s11263-016-0930-5 doi (DE-627)OLC2057750760 (DE-He213)s11263-016-0930-5-p DE-627 ger DE-627 rakwb eng 004 VZ Gu, Shuhang verfasserin aut Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. Low rank analysis Nuclear norm minimization Low level vision Xie, Qi aut Meng, Deyu aut Zuo, Wangmeng aut Feng, Xiangchu aut Zhang, Lei aut Enthalten in International journal of computer vision Springer US, 1987 121(2016), 2 vom: 18. Juli, Seite 183-208 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:121 year:2016 number:2 day:18 month:07 pages:183-208 https://doi.org/10.1007/s11263-016-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 GBV_ILN_4046 AR 121 2016 2 18 07 183-208 |
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10.1007/s11263-016-0930-5 doi (DE-627)OLC2057750760 (DE-He213)s11263-016-0930-5-p DE-627 ger DE-627 rakwb eng 004 VZ Gu, Shuhang verfasserin aut Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. Low rank analysis Nuclear norm minimization Low level vision Xie, Qi aut Meng, Deyu aut Zuo, Wangmeng aut Feng, Xiangchu aut Zhang, Lei aut Enthalten in International journal of computer vision Springer US, 1987 121(2016), 2 vom: 18. Juli, Seite 183-208 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:121 year:2016 number:2 day:18 month:07 pages:183-208 https://doi.org/10.1007/s11263-016-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 GBV_ILN_4046 AR 121 2016 2 18 07 183-208 |
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10.1007/s11263-016-0930-5 doi (DE-627)OLC2057750760 (DE-He213)s11263-016-0930-5-p DE-627 ger DE-627 rakwb eng 004 VZ Gu, Shuhang verfasserin aut Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. Low rank analysis Nuclear norm minimization Low level vision Xie, Qi aut Meng, Deyu aut Zuo, Wangmeng aut Feng, Xiangchu aut Zhang, Lei aut Enthalten in International journal of computer vision Springer US, 1987 121(2016), 2 vom: 18. Juli, Seite 183-208 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:121 year:2016 number:2 day:18 month:07 pages:183-208 https://doi.org/10.1007/s11263-016-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 GBV_ILN_4046 AR 121 2016 2 18 07 183-208 |
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10.1007/s11263-016-0930-5 doi (DE-627)OLC2057750760 (DE-He213)s11263-016-0930-5-p DE-627 ger DE-627 rakwb eng 004 VZ Gu, Shuhang verfasserin aut Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. Low rank analysis Nuclear norm minimization Low level vision Xie, Qi aut Meng, Deyu aut Zuo, Wangmeng aut Feng, Xiangchu aut Zhang, Lei aut Enthalten in International journal of computer vision Springer US, 1987 121(2016), 2 vom: 18. Juli, Seite 183-208 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:121 year:2016 number:2 day:18 month:07 pages:183-208 https://doi.org/10.1007/s11263-016-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 GBV_ILN_4046 AR 121 2016 2 18 07 183-208 |
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10.1007/s11263-016-0930-5 doi (DE-627)OLC2057750760 (DE-He213)s11263-016-0930-5-p DE-627 ger DE-627 rakwb eng 004 VZ Gu, Shuhang verfasserin aut Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. Low rank analysis Nuclear norm minimization Low level vision Xie, Qi aut Meng, Deyu aut Zuo, Wangmeng aut Feng, Xiangchu aut Zhang, Lei aut Enthalten in International journal of computer vision Springer US, 1987 121(2016), 2 vom: 18. Juli, Seite 183-208 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:121 year:2016 number:2 day:18 month:07 pages:183-208 https://doi.org/10.1007/s11263-016-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 GBV_ILN_4046 AR 121 2016 2 18 07 183-208 |
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Gu, Shuhang |
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10.1007/s11263-016-0930-5 |
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weighted nuclear norm minimization and its applications to low level vision |
| title_auth |
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision |
| abstract |
Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. © Springer Science+Business Media New York 2016 |
| abstractGer |
Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. © Springer Science+Business Media New York 2016 |
| abstract_unstemmed |
Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting. © Springer Science+Business Media New York 2016 |
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Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision |
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Xie, Qi Meng, Deyu Zuo, Wangmeng Feng, Xiangchu Zhang, Lei |
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Xie, Qi Meng, Deyu Zuo, Wangmeng Feng, Xiangchu Zhang, Lei |
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