Efficient Inversion of the Cone Beam Transform for a General Class of Curves

We extend an efficient cone beam transform inversion formula, proposed earlier by one of the authors for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much, and do not admit lines which are tangent to C at one point and intersect C at another point. The notions of PI-lines and PI-segments are generalized, their properties are studied. The domain U is found, where PI-lines are guaranteed to be unique. Results of numerical experiments demonstrate very good image quality.