From rank estimation to rank approximation : rank residual constraint for image restoration

In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underly...

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Main Authors: Zha, Zhiyuan, Yuan, Xin, Wen, Bihan, Zhou, Jiantao, Zhang, Jiachao, Zhu, Ce
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2021
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Online Access:https://hdl.handle.net/10356/154487
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1544872021-12-23T06:59:26Z From rank estimation to rank approximation : rank residual constraint for image restoration Zha, Zhiyuan Yuan, Xin Wen, Bihan Zhou, Jiantao Zhang, Jiachao Zhu, Ce School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Low-Rank Rank Residual Constraint In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observation, we progressively approximate (approach) the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Toward this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual qualities. Ministry of Education (MOE) This work was supported in part by the NSFC under Grant 61571102, in part by the Applied Research Programs of Science and Technology, Sichuan, under Grant 2018JY0035, in part by the Ministry of Education, Singapore, through the Start-Up Grant, and in part by the Macau Science and Technology Development Fund, Macau SAR, under Grant SKL-IOTSC-2018-2020, Grant 077/2018/A2, and Grant 022/2017/A1. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Chia-Kai Liang. 2021-12-23T06:59:26Z 2021-12-23T06:59:26Z 2019 Journal Article Zha, Z., Yuan, X., Wen, B., Zhou, J., Zhang, J. & Zhu, C. (2019). From rank estimation to rank approximation : rank residual constraint for image restoration. IEEE Transactions On Image Processing, 29, 3254-3269. https://dx.doi.org/10.1109/TIP.2019.2958309 1057-7149 https://hdl.handle.net/10356/154487 10.1109/TIP.2019.2958309 31841410 2-s2.0-85079574523 29 3254 3269 en SKL-IOTSC-2018-2020 077/2018/A2 022/2017/A1 IEEE Transactions on Image Processing © 2019 IEEE. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Low-Rank
Rank Residual Constraint
spellingShingle Engineering::Electrical and electronic engineering
Low-Rank
Rank Residual Constraint
Zha, Zhiyuan
Yuan, Xin
Wen, Bihan
Zhou, Jiantao
Zhang, Jiachao
Zhu, Ce
From rank estimation to rank approximation : rank residual constraint for image restoration
description In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observation, we progressively approximate (approach) the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Toward this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual qualities.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Zha, Zhiyuan
Yuan, Xin
Wen, Bihan
Zhou, Jiantao
Zhang, Jiachao
Zhu, Ce
format Article
author Zha, Zhiyuan
Yuan, Xin
Wen, Bihan
Zhou, Jiantao
Zhang, Jiachao
Zhu, Ce
author_sort Zha, Zhiyuan
title From rank estimation to rank approximation : rank residual constraint for image restoration
title_short From rank estimation to rank approximation : rank residual constraint for image restoration
title_full From rank estimation to rank approximation : rank residual constraint for image restoration
title_fullStr From rank estimation to rank approximation : rank residual constraint for image restoration
title_full_unstemmed From rank estimation to rank approximation : rank residual constraint for image restoration
title_sort from rank estimation to rank approximation : rank residual constraint for image restoration
publishDate 2021
url https://hdl.handle.net/10356/154487
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