Theoretically exact filtered backprojection-type inversion algorithm for spiral CT

Proposed is a theoretically exact formula for inversion of data obtained by a spiral computed tomography ( CT) scan with a two- dimensional detector array. The detector array is supposed to be of limited extent in the axial direction. The main property of the formula is that it can be implemented in a truly filtered backprojection fashion. First, one performs shift- invariant filtering of a derivative of the cone beam projections, and, second, the result is backprojected in order to form an image. Another property is that the formula solves the so- called long object problem. Limitations of the algorithm are discussed. Results of numerical experiments are presented.