A flexible iterative method for 3D reconstruction from X-ray projections

The problem of reconstructing a 3D image of an object from a few number of X-ray projections is highly underdetermined. We propose a flexible method based on the regularization of the inverse linear problem with a general quadratic criterion. The minimization is performed by an iterative algorithm with a Gauss-Seidel behaviour. Due to the discrete smooth interpolation formulation, additional linear constraints are inserted, and the method is ensured to converge to the unique minimum. The application of this method is shown for 3D reconstruction of cerebral blood vessels from six projections, and the effect of various criteria is compared to the result of other algebraic methods.