Abbreviated Journal Title
SIAM J. Appl. Math.
shift-invariant filtering; theoretically exact; PI lines; LONG-OBJECT PROBLEM; IMAGE-RECONSTRUCTION; COMPUTED-TOMOGRAPHY; SPIRAL; CT; ALGORITHM; PROJECTION; CIRCLE; PITCH; Mathematics, Applied
We extend a cone beam transform inversion formula, proposed earlier for helices by one of the authors, to a general class of curves. The inversion formula remains efficient, because filtering is shift-invariant and is performed along a one-parametric family of lines. 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, and 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.
Siam Journal on Applied Mathematics
Katsevich, Alexander and Kapralov, Mikhail, "Filtered backprojection inversion of the cone beam transform for a general class of curves" (2007). Faculty Bibliography 2000s. 7289.