Based on the linearity of the Radon transform and the convolution-backprojection reconstruction algorithm, a new linear-vector space notation is introduced that is of general use in computed tomography (CT). Using this notation, a consistency condition for the completion of incomplete projection data is described. This consistency condition leads to singular or ill-conditioned systems of linear equations for the unknown projection data. Using regularization methods, an algorithm for the consistent projection completion is presented that can exploit symmetries of the missing data region. The performance of the new algorithm is documented with simulated and actualy measured CT-projection data. The algorithm quantitatively improves CT reconstructions with realistic amounts of data and noise and can be used for the completion of arbitrary regions of missing projections.
© 1985 Optical Society of America
P. Seitz and P. Rüegsegger, "Reconstruction algorithm for incomplete projections in the framework of linear operators in normed linear spaces," J. Opt. Soc. Am. A 2, 1667-1676 (1985)