Numerical Backprojection in the Inverse 3D Radon Transform
In this paper we study the error caused by numerically approximating the integral over the sphere in three dimensions as part of Radon’s inversion formula. Using special functions we demonstrate that, if suitable filters in the first reconstruction step — differenciation of order two — are used, essential errors are produced only outside the region of interest. The directions needed in measuring the data fulfil also another requirement, they guarantee optimal resolution in the reconstruction.
KeywordsDiscrete Fourier Transform Integration Formula Inverse Fourier Transform Inversion Formula Exact Integration
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