# Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography.

Trampert, Patrick; Vogelgesang, Jonas; Schorr, Christian; Maisl, Michael; Bogachev, Sviatoslav; Marniok, Nico; Louis, Alfred; Dahmen, Tim; Slusallek, Philipp

Spherically symmetric volume elements (blobs) were evaluated as basis functions for iterative tomographic reconstructions in computed laminography. We implemented an iterative algorithm for the computation of three-dimensional reconstructions from computed laminography projections based on the simultaneous algebraic reconstruction technique also known as SART. Hereby, the discretization of the volume was realized by means of blobs based on generalized Kaiser-Bessel window functions. We found that band-limiting properties of blob functions are beneficial compared to a voxel basis particular in the case of noisy projections and if only a limited number of projections is available. In this case, using blob basis functions leads to sharper 3D datasets with less artifacts, which improves the capability to detect small features in images such as defects. The increased computational demand per iteration of the algorithm is compensated for by a faster convergence rate when using blobs, such that the overall performance of the tomographic reconstruction is approximately identical for blob as well as voxel basis functions. We conclude that despite the higher complexity, tomographic reconstruction from computed laminography data should be implemented using blob basis functions, especially if noisy data is expected.

In *Journal of X-Ray Science and Technology, 25(4): 533-546, 2017*