Academic Journal
View in EDS

Newton-SOR method for fast statistical tomographic image reconstruction.

Bibliographic Details
Title: Newton-SOR method for fast statistical tomographic image reconstruction.
Authors: Kudo, Hiroyuki1, Sawada, Shinji2
Source: Systems & Computers in Japan. 4/1/2003, Vol. 34 Issue 4, p1-11. 11p.
Subject Terms: Image reconstruction, Computational complexity, MAP (Computer program language), Iterative methods (Mathematics), Image processing, Electronic data processing
Abstract: There are recent studies on image reconstruction for emission CT and transmission CT, using the maximum likelihood (ML) estimation or the maximum a posteriori (MAP) estimation, aiming at quality improvement of the reconstructed image. Those methods in general have the problem that minimization of the convex cost function by iterations is required, which increases the computational complexity. This paper proposes a new image reconstruction method, which requires less computation per iteration and realizes a fast convergence. The proposed method is based on the principle that the convex cost function is approximated in the iteration by a quadratic function, and the value of the quadratic function is reduced by SOR method, which is the solution procedure for the linear equation. The method can be called the Newton-SOR method in the sense that both methods are combined. In order to guarantee global convergence of the Newton-SOR method, mathematical techniques, called trust region and line search methods, are used, and the projection SOR method with the nonnegative condition is used, where a negative value appearing in the iteration is replaced by zero. The proposed method satisfies all of the desired properties of the iteration method as follows. (1) The convergence to the true solution minimizing the cost function is guaranteed. (2) The computational complexity per iteration is less, and a fast convergence is realized. (3) The method can be applied in a unified way to a wide range of convex cost functions. (4) The nonnegative condition can be handled easily. The effectiveness of the proposed method is demonstrated by a simulation experiment. The result of application to the clinical PET data is also shown. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(4): 1–11, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10178 [ABSTRACT FROM AUTHOR]
Database: Supplemental Index
FullText Links:
  – Type: other
Text:
  Availability: 0
Header DbId: edo
DbLabel: Supplemental Index
An: 13508551
RelevancyScore: 832
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 831.768432617188
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Newton-SOR method for fast statistical tomographic image reconstruction.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kudo%2C+Hiroyuki%22">Kudo, Hiroyuki</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Sawada%2C+Shinji%22">Sawada, Shinji</searchLink><relatesTo>2</relatesTo>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Systems+%26+Computers+in+Japan%22">Systems & Computers in Japan</searchLink>. 4/1/2003, Vol. 34 Issue 4, p1-11. 11p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Image+reconstruction%22">Image reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22MAP+%28Computer+program+language%29%22">MAP (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Image+processing%22">Image processing</searchLink><br /><searchLink fieldCode="DE" term="%22Electronic+data+processing%22">Electronic data processing</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: There are recent studies on image reconstruction for emission CT and transmission CT, using the maximum likelihood (ML) estimation or the maximum a posteriori (MAP) estimation, aiming at quality improvement of the reconstructed image. Those methods in general have the problem that minimization of the convex cost function by iterations is required, which increases the computational complexity. This paper proposes a new image reconstruction method, which requires less computation per iteration and realizes a fast convergence. The proposed method is based on the principle that the convex cost function is approximated in the iteration by a quadratic function, and the value of the quadratic function is reduced by SOR method, which is the solution procedure for the linear equation. The method can be called the Newton-SOR method in the sense that both methods are combined. In order to guarantee global convergence of the Newton-SOR method, mathematical techniques, called trust region and line search methods, are used, and the projection SOR method with the nonnegative condition is used, where a negative value appearing in the iteration is replaced by zero. The proposed method satisfies all of the desired properties of the iteration method as follows. (1) The convergence to the true solution minimizing the cost function is guaranteed. (2) The computational complexity per iteration is less, and a fast convergence is realized. (3) The method can be applied in a unified way to a wide range of convex cost functions. (4) The nonnegative condition can be handled easily. The effectiveness of the proposed method is demonstrated by a simulation experiment. The result of application to the clinical PET data is also shown. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(4): 1–11, 2003; Published online in Wiley InterScience (<URL>www.interscience.wiley.com</URL>). DOI 10.1002/scj.10178 [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edo&AN=13508551
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/scj.10178
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 1
    Subjects:
      – SubjectFull: Image reconstruction
        Type: general
      – SubjectFull: Computational complexity
        Type: general
      – SubjectFull: MAP (Computer program language)
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Image processing
        Type: general
      – SubjectFull: Electronic data processing
        Type: general
    Titles:
      – TitleFull: Newton-SOR method for fast statistical tomographic image reconstruction.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kudo, Hiroyuki
      – PersonEntity:
          Name:
            NameFull: Sawada, Shinji
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 04
              Text: 4/1/2003
              Type: published
              Y: 2003
          Identifiers:
            – Type: issn-print
              Value: 08821666
          Numbering:
            – Type: volume
              Value: 34
            – Type: issue
              Value: 4
          Titles:
            – TitleFull: Systems & Computers in Japan
              Type: main
ResultId 1