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A new constrained total variational deblurring model and its fast algorithm

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A new constrained total variational deblurring model and its fast algorithm. / Williams, Bryan Michael; Chen, Ke; Harding, Simon P.
In: Numerical Algorithms, Vol. 69, No. 2, 29.06.2015, p. 415-441.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Williams, BM, Chen, K & Harding, SP 2015, 'A new constrained total variational deblurring model and its fast algorithm', Numerical Algorithms, vol. 69, no. 2, pp. 415-441. https://doi.org/10.1007/s11075-014-9904-2

APA

Williams, B. M., Chen, K., & Harding, S. P. (2015). A new constrained total variational deblurring model and its fast algorithm. Numerical Algorithms, 69(2), 415-441. https://doi.org/10.1007/s11075-014-9904-2

Vancouver

Williams BM, Chen K, Harding SP. A new constrained total variational deblurring model and its fast algorithm. Numerical Algorithms. 2015 Jun 29;69(2):415-441. doi: 10.1007/s11075-014-9904-2

Author

Williams, Bryan Michael ; Chen, Ke ; Harding, Simon P. / A new constrained total variational deblurring model and its fast algorithm. In: Numerical Algorithms. 2015 ; Vol. 69, No. 2. pp. 415-441.

Bibtex

@article{97e87228ed9a4348832bb44455b293fb,
title = "A new constrained total variational deblurring model and its fast algorithm",
abstract = "Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.",
keywords = "Alternating direction method of multipliers, Box constraint, Image deblurring, Total variation, Transforms",
author = "Williams, {Bryan Michael} and Ke Chen and Harding, {Simon P.}",
year = "2015",
month = jun,
day = "29",
doi = "10.1007/s11075-014-9904-2",
language = "English",
volume = "69",
pages = "415--441",
journal = "Numerical Algorithms",
issn = "1017-1398",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - A new constrained total variational deblurring model and its fast algorithm

AU - Williams, Bryan Michael

AU - Chen, Ke

AU - Harding, Simon P.

PY - 2015/6/29

Y1 - 2015/6/29

N2 - Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.

AB - Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.

KW - Alternating direction method of multipliers

KW - Box constraint

KW - Image deblurring

KW - Total variation

KW - Transforms

U2 - 10.1007/s11075-014-9904-2

DO - 10.1007/s11075-014-9904-2

M3 - Journal article

AN - SCOPUS:84929944019

VL - 69

SP - 415

EP - 441

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

IS - 2

ER -