RECONSTRUCTION OF TOMOGRAPHIC IMAGES FROM PROJECTIONS OF A SMALL NUMBER OF VIEWS VIA MATHEMATICAL PROGRAMMING.

This paper discusses reconstruction by mathematical programming, where the general tomogram is to be reconstructed from the projection data of a few views without imposing the condition of circular symmetry or periodicity. A system of linear equations is formulated from the X-ray projections of a few number of views considering the virtual pixels passed by the X-ray beam. Then the tomogram is reconstructed by determining the optimal solution minimizing the sum of absolute values of residual or square residuals by linear programming or by quadratic programming. An accurate solution is obtained by a relatively simple computation procedure and by a finite number of iterations. The relation between the number of pixels and the iterations to reach the convergence is examined. The usefulness of the method is verified by computer simulation. The effects of the noise in the projection data and the resolution of the X-ray detector on the reconstructed image are also examined by the simulation.