Fast 3D algorithm for reconstructing edges of a function from truncated spiral cone beam data

Proposed is an algorithm for computing a function f₀ which retains most of the sharp features of f knowing truncated cone-beam projections of f. It is shown that f₀=Bf, where the principal symbol of operator B is close to one. The symbol of B is singular, and this leads to artifacts: in general, singsupp(f₀)⊄singsupp(f). The algorithm for computing f ₀ is efficient and of the filtered-backprojection type. Results of a numerical experiment are presented. They show that discontinuities of f are clearly visible in images of f₀. Coronal, sagittal, and transverse cross-sections of f₀ have nearly identical spatial resolution despite relatively large pitch. Artifacts, which are due to the nonsmoothness of the symbol of B, are hardly visible