ON MATHEMATICAL PROBLEMS OF TWO-DIMENSIONAL TOMOGRAPHY

摘要

In this paper the problem of restoring the inside construction of an object by its X-ray pictures is considered. We limit ourself on discussing the two dimensional case. Let us note that just this case is tised in acting medical tomography devices. The problem is to find the formulas, which as good as possible restore the density, having on hand the X-ray pictures for a finite number of directions only and which are steady for L_2(-1,1) distortions of the projections.