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13 September 2005 A solution to arc correction in cylindrical PET scanner
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For a PET scanner with circular array of detectors, the width of line-of-response (LOR) decreases as the distance between the LOR and the center increases. The decrease of width of the LOR leads to problem of non-uniform and under sampling of projections. The consequence of non-uniform sampling is the distortion of high frequency reconstructed images or loss of fine detail. Correcting this non-uniform sampling problem is known as arc-correction. The purpose of this study is to create the best estimate of non-uniformly sampled projections from uniformly spaced sets of LOR. Four polynomial type interpolating algorithms: Lagrange, iterative Neville, natural cubic spline and clamped cubic spline are used to get the best estimate of projections. A set of simulated projections are generated. The simulated projections are divided into two sets: the first set has 10 functions of pulses such that f11 has one pulse, f12 has two pulses and so on. In the second set f21 has one triangular pulse, f22 has two triangular pulses and so on. For each group interpolated data is compared to the original data. In addition, one projection of a 20cm FDG filled disk is used for comparison with simulated data. It is shown that clamped and natural cubic spline accuracy is superior to the other three algorithms in every case but Lagrange outperforms other algorithms for the speed of execution.
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Babak Farsaii "A solution to arc correction in cylindrical PET scanner", Proc. SPIE 5916, Mathematical Methods in Pattern and Image Analysis, 59160Y (13 September 2005);

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