An efficient multi-grid method for TV minimization problems

Zhenwei  Zhang; Xue Li; Yuping Duan; Ke Yin; Xue-Cheng Tai

doi:10.3934/ipi.2021034

An efficient multi-grid method for TV minimization problems

Zhenwei Zhang, Xue Li, Yuping Duan^*, Ke Yin^*, Xue-Cheng Tai

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

We propose an efficient multi-grid domain decomposition method for solving the total variation (TV) minimization problems. Our multi-grid scheme is developed based on the piecewise constant function spanned subspace correction rather than the piecewise linear one in [17], which ensures the calculation of the TV term only occurs on the boundaries of the support sets. Besides, the domain decomposition method is implemented on each layer to enable parallel computation. Comprehensive comparison results are presented to demonstrate the improvement in CPU time and image quality of the proposed method on medium and large-scale image denoising and reconstruction problems.

Original language	English
Pages (from-to)	1199-1221
Number of pages	23
Journal	Inverse Problems and Imaging
Volume	15
Issue number	5
Early online date	Apr 2021
DOIs	https://doi.org/10.3934/ipi.2021034
Publication status	Published - Oct 2021

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title = "An efficient multi-grid method for TV minimization problems",

abstract = "We propose an efficient multi-grid domain decomposition method for solving the total variation (TV) minimization problems. Our multi-grid scheme is developed based on the piecewise constant function spanned subspace correction rather than the piecewise linear one in [17], which ensures the calculation of the TV term only occurs on the boundaries of the support sets. Besides, the domain decomposition method is implemented on each layer to enable parallel computation. Comprehensive comparison results are presented to demonstrate the improvement in CPU time and image quality of the proposed method on medium and large-scale image denoising and reconstruction problems.",

author = "Zhenwei Zhang and Xue Li and Yuping Duan and Ke Yin and Xue-Cheng Tai",

note = "The work of the first three authors were supported by NSFC 11701418 and 12071345, Major Science and Technology Project of Tianjin 18ZXRHSY00160 and Recruitment Program of Global Young Expert. The work of Yin was supported by NSFC 11801200 and a startup grant from HUST. The work of the last author was supported by Hong Kong Baptist University startup grants RG(R)-RC/17-18/02-MATH and FRG2/17-18/033. ",

year = "2021",

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doi = "10.3934/ipi.2021034",

language = "English",

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publisher = "American Institute of Mathematical Sciences",

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T1 - An efficient multi-grid method for TV minimization problems

AU - Zhang, Zhenwei

AU - Li, Xue

AU - Duan, Yuping

AU - Yin, Ke

AU - Tai, Xue-Cheng

N1 - The work of the first three authors were supported by NSFC 11701418 and 12071345, Major Science and Technology Project of Tianjin 18ZXRHSY00160 and Recruitment Program of Global Young Expert. The work of Yin was supported by NSFC 11801200 and a startup grant from HUST. The work of the last author was supported by Hong Kong Baptist University startup grants RG(R)-RC/17-18/02-MATH and FRG2/17-18/033.

PY - 2021/10

Y1 - 2021/10

N2 - We propose an efficient multi-grid domain decomposition method for solving the total variation (TV) minimization problems. Our multi-grid scheme is developed based on the piecewise constant function spanned subspace correction rather than the piecewise linear one in [17], which ensures the calculation of the TV term only occurs on the boundaries of the support sets. Besides, the domain decomposition method is implemented on each layer to enable parallel computation. Comprehensive comparison results are presented to demonstrate the improvement in CPU time and image quality of the proposed method on medium and large-scale image denoising and reconstruction problems.

AB - We propose an efficient multi-grid domain decomposition method for solving the total variation (TV) minimization problems. Our multi-grid scheme is developed based on the piecewise constant function spanned subspace correction rather than the piecewise linear one in [17], which ensures the calculation of the TV term only occurs on the boundaries of the support sets. Besides, the domain decomposition method is implemented on each layer to enable parallel computation. Comprehensive comparison results are presented to demonstrate the improvement in CPU time and image quality of the proposed method on medium and large-scale image denoising and reconstruction problems.

U2 - 10.3934/ipi.2021034

DO - 10.3934/ipi.2021034

M3 - Journal article

SN - 1930-8337

VL - 15

SP - 1199

EP - 1221

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 5

ER -

An efficient multi-grid method for TV minimization problems

Abstract

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