Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations

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The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the ... continued below

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Pages: 10

Creation Information

Tam, K.C. & Perez-Mendez, V. December 1, 1979.

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  • Lawrence Berkeley Laboratory
    Publisher Info: California Univ., Berkeley (USA). Lawrence Berkeley Lab.
    Place of Publication: Berkeley, California

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Description

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables.

Physical Description

Pages: 10

Notes

Dep. NTIS, PC A02/MF A01.

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  • International optical computing conference, Washington, DC, USA, 7 Apr 1980

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  • Report No.: LBL-10207
  • Report No.: CONF-800453-2
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 5404963
  • Archival Resource Key: ark:/67531/metadc1064127

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • December 1, 1979

Added to The UNT Digital Library

  • Feb. 4, 2018, 10:51 a.m.

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  • April 24, 2018, 4:46 p.m.

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Tam, K.C. & Perez-Mendez, V. Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations, article, December 1, 1979; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1064127/: accessed August 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.