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Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring.

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Τίτλος: Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring.
Συγγραφείς: O'Connor, Daniel, Vandenberghe, Lieven
Πηγή: SIAM Journal on Imaging Sciences; 2014, Vol. 7 Issue 3, p1724-1754, 31p
Θεματικοί όροι: Image processing, Monotone operators, Boundary value problems, Convex programming, Algorithm research
Περίληψη: We present primal-dual decomposition algorithms for convex optimization problems with cost functions f(x) + g(Ax), where f and g have inexpensive proximal operators and A can be decomposed as a sum of two structured matrices. The methods are based on the Douglas--Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image deblurring problems with nonquadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the primal-dual splitting approach allows us to handle general boundary conditions for the blurring operator. Numerical results indicate that the primal-dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas--Rachford algorithm applied to a reformulated primal problem, and the Chambolle--Pock primal-dual algorithm. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Imaging Sciences is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring.
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  Data: <searchLink fieldCode="AR" term="%22O'Connor%2C+Daniel%22">O'Connor, Daniel</searchLink><br /><searchLink fieldCode="AR" term="%22Vandenberghe%2C+Lieven%22">Vandenberghe, Lieven</searchLink>
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  Data: SIAM Journal on Imaging Sciences; 2014, Vol. 7 Issue 3, p1724-1754, 31p
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  Data: <searchLink fieldCode="DE" term="%22Image+processing%22">Image processing</searchLink><br /><searchLink fieldCode="DE" term="%22Monotone+operators%22">Monotone operators</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+programming%22">Convex programming</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithm+research%22">Algorithm research</searchLink>
– Name: Abstract
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  Data: We present primal-dual decomposition algorithms for convex optimization problems with cost functions f(x) + g(Ax), where f and g have inexpensive proximal operators and A can be decomposed as a sum of two structured matrices. The methods are based on the Douglas--Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image deblurring problems with nonquadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the primal-dual splitting approach allows us to handle general boundary conditions for the blurring operator. Numerical results indicate that the primal-dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas--Rachford algorithm applied to a reformulated primal problem, and the Chambolle--Pock primal-dual algorithm. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Imaging Sciences is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1137/13094671X
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 31
        StartPage: 1724
    Subjects:
      – SubjectFull: Image processing
        Type: general
      – SubjectFull: Monotone operators
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Convex programming
        Type: general
      – SubjectFull: Algorithm research
        Type: general
    Titles:
      – TitleFull: Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring.
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            NameFull: O'Connor, Daniel
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            NameFull: Vandenberghe, Lieven
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            – D: 01
              M: 09
              Text: 2014
              Type: published
              Y: 2014
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              Value: 7
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            – TitleFull: SIAM Journal on Imaging Sciences
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