Backprojection inverse filtration for laminographic reconstruction

Traditional tomography uses circular trajectories and here, filtered backprojection often works well. However, for objects with large aspect rations, rotational tomography is often not feasible. In these cases, other trajectories can be more appropriate. For generic trajectories filtered backprojection methods might not work well and full iterative reconstruction can be computationally demanding. In this paper we thus propose a third paradigm that combines aspects of both of these techniques. We use interpolation and backprojection techniques to generate an initial estimate of an object's internal structure using projection images taken at different orientations. Depending on the scanning geometry used to calculate the tomographic projections, this initial estimate can be understood as a blurred (filtered) approximation of the actual structure. For each scanning geometry, we specify the equivalent blurring operator that would provide the same estimate directly from a representation of the object's internal structure. We then use iterative techniques to invert this filtering operation, thus estimating the internal structure from the estimate of its blurred representation