Estimation of geometrical parameters for fan beam tomography

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Abstract
Tomographic image quality depends on precisely determining the geometric parameters that reference the detector system to the transaxial imaging coordinate system. In addition to the projection of the centre of rotation onto the detector, fan beam geometry requires two other parameters that include the focal length and the projection of the focal point onto the detector. Heretofore no method has been developed for estimating the geometrical parameters of a fan beam detector system. A method is presented for estimating these parameters from centroids of the measured projections of a point source using the non-linear estimation algorithm due to Marquardt. The technique is applied to single photon emission computed tomography (SPECT) data from a rotating gamma camera using a fan beam collimator. The parameters can be determined very quickly in a clinical environment. The corresponding reconstructed images do not show image artefacts or loss of resolution characteristic of inaccurately determined geometric parameters.