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An Efficient Truncated Nuclear Norm Constrained Matrix Completion For Image Inpainting

Published: 11 June 2018 Publication History

Abstract

The matrix completion problem has found many applications in image and graphics fields. Developing fast and exact algorithms still remains challenging. The truncated nuclear norm (TNN), taking advantage of priori target rank information, is known as a better surrogate function to the rank constraint than the traditional nuclear norm. However, the TNN penalized algorithms always converge slowly due to the two-step scheme for avoiding directly updating the noncovex functions. In this paper, we propose a computationally efficient algorithm, Momentum Adaptive and Rank Revealing (MARR), for the TNN regularized matrix completion problem. The distinct advantages are to (1) reduce iterations by introducing non-monotonic constraints, and (2) decrease computational burden by controlling the size of matrix. Moreover, the descent property and convergence of the search are proven. Experiments on image inpainting, including images and range data, show that the proposed algorithm achieves very competitive results visually and numerically compared to several state-of-the-art approaches, while providing substantial reduction of iterations and runtime, thereby more applicable in real-world problems.

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Cited By

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  • (2022)DKH: a hybridized approach for image inpainting using Bayes probabilistic-based image fusionInternational Journal of Intelligent Robotics and Applications10.1007/s41315-022-00267-77:1(149-163)Online publication date: 10-Dec-2022
  • (2022)Performance Evaluation of Biharmonic Function-Based Image Inpainting ApproachICT with Intelligent Applications10.1007/978-981-19-3571-8_45(475-483)Online publication date: 1-Oct-2022
  • (2020) Truncated Low-Rank and Total p Variation Constrained Color Image Completion and its Moreau Approximation Algorithm IEEE Transactions on Image Processing10.1109/TIP.2020.300836729(7861-7874)Online publication date: 2020

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  1. An Efficient Truncated Nuclear Norm Constrained Matrix Completion For Image Inpainting

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    cover image ACM Other conferences
    CGI 2018: Proceedings of Computer Graphics International 2018
    June 2018
    284 pages
    ISBN:9781450364010
    DOI:10.1145/3208159
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 11 June 2018

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    Author Tags

    1. Accelerated proximal gradient
    2. Image inpainting
    3. Matrix completion
    4. Singular value thresholding
    5. Truncated nuclear norm

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    CGI 2018
    CGI 2018: Computer Graphics International 2018
    June 11 - 14, 2018
    Island, Bintan, Indonesia

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    CGI 2018 Paper Acceptance Rate 35 of 159 submissions, 22%;
    Overall Acceptance Rate 35 of 159 submissions, 22%

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    Cited By

    View all
    • (2022)DKH: a hybridized approach for image inpainting using Bayes probabilistic-based image fusionInternational Journal of Intelligent Robotics and Applications10.1007/s41315-022-00267-77:1(149-163)Online publication date: 10-Dec-2022
    • (2022)Performance Evaluation of Biharmonic Function-Based Image Inpainting ApproachICT with Intelligent Applications10.1007/978-981-19-3571-8_45(475-483)Online publication date: 1-Oct-2022
    • (2020) Truncated Low-Rank and Total p Variation Constrained Color Image Completion and its Moreau Approximation Algorithm IEEE Transactions on Image Processing10.1109/TIP.2020.300836729(7861-7874)Online publication date: 2020

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