Accurate and artifact free reconstruction of tomographic images requires precise knowledge of the imaging system geometry. This work proposes a novel projection matrix (P-matrix) based calibration method to enable C-arm inverse geometry CT (IGCT). The method is evaluated for scanning-beam digital x-ray (SBDX), a C-arm mounted inverse geometry fluoroscopic technology. A helical configuration of fiducials is imaged at each gantry angle in a rotational acquisition. For each gantry angle, digital tomosynthesis is performed at multiple planes and a composite image analogous to a cone-beam projection is generated from the plane stack. The geometry of the C-arm, source array, and detector array is determined at each angle by constructing a parameterized 3D-to-2D projection matrix that minimizes the sum-of-squared deviations between measured and projected fiducial coordinates. Simulations were used to evaluate calibration performance with translations and rotations of the source and detector. In a geometry with 1 mm translation of the central ray relative to the axis-of-rotation and 1 degree yaw of the detector and source arrays, the maximum error in the recovered translational parameters was 0.4 mm and maximum error in the rotation parameter was 0.02 degrees. The relative root-mean-square error in a reconstruction of a numerical thorax phantom was 0.4% using the calibration method, versus 7.7% without calibration. Changes in source-detector-distance were the most challenging to estimate. Reconstruction of experimental SBDX data using the proposed method eliminated double contour artifacts present in a non-calibrated reconstruction. The proposed IGCT geometric calibration method reduces image artifacts when uncertainties exist in system geometry.
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