Limited-Angle Three-Dimensional Reconstructions Using Fourier Transform Iterations And Radon Transform Iterations

Kwok-Cheong Tam; Victor Perez-Mendez

doi:10.1117/12.7972766

1 August 1981 Limited-Angle Three-Dimensional Reconstructions Using Fourier Transform Iterations And Radon Transform Iterations

Kwok-Cheong Tam, Victor Perez-Mendez

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Optical Engineering, Vol. 20, Issue 4, 204586 (August 1981). https://doi.org/10.1117/12.7972766

Abstract

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 has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been 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 which 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.

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Kwok-Cheong Tam and Victor Perez-Mendez "Limited-Angle Three-Dimensional Reconstructions Using Fourier Transform Iterations And Radon Transform Iterations," Optical Engineering 20(4), 204586 (1 August 1981). https://doi.org/10.1117/12.7972766

Published: 1 August 1981

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