THE SPHERE METHOD FOR THE INVERSE PROBLEMS OF THE RADON TRANSFORMS

Using a different method - the sphere method, which is based on the technique of changing the integral on a plane into the integral on a hemisphere, we give some concise inverse formulas of the Radon transforms of functions with support in a cone with vertex at the origin and flare angle less than pi/2, or with compact support. These formulas are easy for the computer to operate and thus can be applied in the imaging techniques of computerized tomography.